A quadratic equation x²+2(3x+p)=0 where p is a constant, has roots a and 2a, where a≠0
(a) find the value of a and of p
(b) hence, from a quadratic equation whose roots are a+1 and a-5


HELP ME PLISS​

Answers

Answer 1

Answer:

a = -2 and p = 4.

Step-by-step explanation:

x²+2(3x+p)=0

x^2 + 6x + 2p = 0

For the general equation ax^2 + bx + c = 0, the sum of roots = -b/a and their product = c / a.

So here we have:

Sum of the roots:

a + 2a = -6/1 = -6

Product of the roots = 2a^2 = 2p/1 = 2p..

So 3a = -6 and

a = -2.

and

2(-2)^2 = 2p

8 = 2p

p = (-2)^2 = 4.

Answer 2

Answer:

see explanation

Step-by-step explanation:

Since x = a and x = 2a are roots, then substitute these values into the equation.

x = a

a² + 2(3a + p) = 0, that is

a² + 6a + 2p = 0 → (1)

x = 2a

(2a)² + 2(3(2a) + p) = 0

4a² + 12a + 2p = 0 → (2)

Solving simultaneously

Subtract (1) from (2) term by term to eliminate p

3a² + 6a = 0 ← in standard form

3a(a + 2) = 0 ← in factored form

Equate each factor to zero and solve for a

3a = 0 ⇒ a = 0

a + 2 = 0 ⇒ a = - 2

Since a ≠ 0 then a = - 2

Substitute a = - 2 into either of the 2 equations and solve for p

substituting into (1)

(- 2)² + 6(- 2) + 2p = 0

4 - 12 + 2p = 0

- 8 + 2p = 0 ( add 8 to both sides )

2p = 8 ( divide both sides by 2 )

p = 4

Thus a = - 2 and p = 4

--------------------------------------------

a + 1 = - 2 + 1 = - 1

a - 5 = - 2 - 5 = - 7

If x = - 1 and x = - 7 are roots then the corresponding factors are

(x + 1) and (x + 7) and the quadratic equation is the product of the factors, that is

(x + 1)(x + 7) = 0 ← expand left side using FOIL

x² + 8x + 7 = 0


Related Questions

Jared started a new job. On the first day he had orientation and worked for 2 hours. On the second day he trained for 4 hours. After that, Jared worked 8 hours each day. If his first paycheck shows that he is being paid for 94 hours of work, how many days did he work a full 8-hour day?

Answers

Answer:

Jared worked 11 days as full 8-hour days.

Step-by-step explanation:

We have:

First day = 2 h

Second day = 4 h

After that = 8 h each day    

Since his paycheck shows 94 hours of work, we can find the number of days that he works 8-hour day:

[tex] 94 h = 2 h + 4 h + 8 h*x [/tex]

Where x is the number of days that he works 8-hours.

[tex] 8 h*x = 88 h [/tex]

[tex] x = \frac{88 h}{8 h} = 11 [/tex]

 

Therefore, Jared worked 11 days as full 8-hour days.

I hope it helps you!                                              



Elsa usually bakes 350 dozen muffins a month. At this rate, how many dozen will she bake in a year ?

Answers

Answer:

4200 dozen

Step-by-step explanation:

One smaller cube labeled with fish food with dimensions of one-quarters feet on each side. Larger cube labeled shipping box with dimensions of length 3 and three-fourths feet; width of 3 feet; height of 3 and one-quarters feet. Part 1: Understanding Volume

Answers

Answer:

Given: Length of smaller cube= 1/4 feet each side

Length of larger cube= 3.75 feet

Width of larger cube= 3 feet

Height of larger cube= 3.25 feet

Step-by-step explanation:

Volume of a cube= length * width * height

Volume of a larger cube= 3.75 * 3 * 3.25 cubic foot

Volume=36.5625 cubic foot

Volume of smaller cube= length * length * length (as length is same on each side)

Volume of smaller cube= 1/4 * 1/4 * 1/4

Volume of smaller cube= 1/64 cubic foot

Hence, volume is calculated.


If a graph fails the vertical line test, what does that mean?
The graph is not a domain.
The graph is not an order pair.
The graph is not a relation.
O The graph is not a function.

Answers

Answer:

the graph is not a function

Step-by-step explanation:

It is not a function because it was more than 1 x value per a y

If Mr.John has a new house he want to put mats on the flour the length of the mat is 95cm and the width is 74cm that is the perimeter of the mat Mr.John has?​

Answers

Answer:

338cm

Step-by-step explanation:

P= 2( L+W)

P=2(95+74)

P=2(169)

P=338cm

Need a little help here pls

Answers

Answer:

The statements that must be true are:

XY and JK form four right angles ⇒ B

XY ⊥ JK ⇒ C

JP = KP ⇒ E

m∠JPX = 90° ⇒ F

Step-by-step explanation:

From the given figure

∵ Line XY is the perpendicular bisector of the line segment JK

→ That means line XY is the line of symmetry of the line segment JK

XY ⊥ JK ⇒ C

∵ XY ∩ JK at point P

P is the midpoint of JK

∵ XY ⊥ JK

∴ ∠JPX, ∠KPX, ∠JPY, and ∠KPY are right angles

XY and JK form four right angles ⇒ B

∵ The measure of the right angle is 90°

∴ m∠JPX = m∠KPX = m∠JPY = m∠KPY = 90°

m∠JPX = 90° ⇒ F

∵ P is the midpoint of JK

JP = KP ⇒ E

which of the following is equivalent to (Cd) to the fifth power

Answers

Answer:

The 3rd option is correct.

Step-by-step explanation:

This is because of an exponent rule that goes:

(xy)^z = x^z(y^z)

The whole thing gets raised to the power. Therefore only the 3rd one works (ps. if you can mark as brainliest that would be amazing, but if not that's fine)

please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!

Answers

Answer:

60

Step-by-step explanation:

The graphs of the equations 4x - y = 6 and x + y = 4 intersect at
the point whose coordinates are

Answers

Answer:

The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are (2,2)

Step-by-step explanation:

The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are?

We need to find the values of x and y by solving the system of equations.

The values of x and y are the point of intersection of those lines.

We have:

[tex]4x - y = 6--eq(1) \\x + y = 4--eq(2)[/tex]

Adding both equations and finding value of x

[tex]4x - y = 6\\ x + y = 4\\-----\\5x+0y=10\\5x=10\\x=\frac{10}{5}\\x=2[/tex]

We get, the value of x: x=2

Now, putting value of x in equation 2 to find value of y:

[tex]x+y=4\\Put\:x=2\\2+y=4\\y=4-2\\y=2[/tex]

So, we get y=2

Therefore we get x=2 and y=2

The solution set is: (2,2)

So, The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are (2,2)

how many sides does a regular polygon have each interior angle of which is measure 120​

Answers

Answer:

12

Step-by-step explanation:

step by step explanation

I think the answer is 6

What is the distance from the top of the iceberg, 6.5 meters above sea level, to the bottom of the iceberg, 52.85 meters below sea level?

Answers

Answer:

I dont know

Step-by-step explanation:

It has to be C because absolute value doesn’t allow you negative answers.

Pleas help me I really need it

Answers

Hello! I hope this helps you!

If you are to simplify the expression, you’d be getting the answer of:

8x-2

before distributing the negative:

(7x2 + 3x) - (8x2 - 5x)

after distributing the negative:

7x2 + 3x - 8x2 + 5x

now add like terms:

7x2 + 3x - 8x2 + 5x

-x2 + 8x

or

8x - x2

-- let me know if you have any questions regarding this.

f(x) = 1/3x -2; reflection in the x-axis

Answers

would it be -1/3x -2?

Please help with this math problem I’ll mark you brainiest

Answers

SRW= 116
SRT= 58
I think, I’m not sure !

I rly need help! I will mark brainliest if you are correct

Answers

Range is 4 dom is 7
Hope that helps

Does anyone know how to do geometry? Please help

Answers

Answer:

No

Step-by-step explanation:

>>>>

i wish i knew. im struggling over here as well

Please help me with this math problem if you can. You just say yes or no if it’s a square, rectangle, etc. and then give the reason why

Answers

The quadrilateral is a rhombus because the diagonals are perpendicular.

HELP PLEASE 50 PT
A chocolate chip cookie recipe calls for 212 cups of sugar. A snicker doodle cookie recipe calls for 314 cups of sugar. How much more sugar, in cups, is in the snicker doodle recipe?**

Answers

Answer:

102 cups

Step-by-step explanation:

314-212=102

102 cups of sugar.

Hope this helps

help please? Find the values of a,b,c,d,e and f

Answers

9514 1404 393

Answer:

a = 30b = 15c = 3d = 30e = 10f = 20

Step-by-step explanation:

The acute angles are all 60°, and the obtuse angles are all the supplement of that, 120°.

Working from the left, we have ...

  a +30 = 60  ⇒  a = 30

  30 +2b = 60  ⇒  b = 15

  5b -5c = 60  ⇒  15 -c = 12  ⇒  c = 3

  10c +d = 60  ⇒  d = 30

  2d +6e = 120  ⇒  60 +6e = 120  ⇒  e = 10

  4f +4e = 120  ⇒  f +10 = 30  ⇒  f = 20

10) 5x + 12 = 4x + 6 = 6

11) −8x − 14 = 7(−2 − 4x) + 4x

12) 16 − 2n = −8 + 4(n − 3)

13) −6(3 − 6r) = −18 + 4r

14) 4(3b − 1) = 9 − b

15) −6x + 7(1 − x) = −4(x − 4)

16) 5 − (8v + 5) = −4(1 + 3v)

17) −8(4 + 4n) = 8(n + 6)

18) 3(a − 6) = −5a − (7 + 3a)

Answers

Answer:

10. -6

11. x=0

12. n=6

13. r=0

14. x=-1

15.x=-1

16.v=-1

17.n-2

18.a=1

Step-by-step explanation:

2x-4=x+6 how solve this

Answers

Answer:

x = 10

Step-by-step explanation:

1. Add 4 to both sides of the equation

2. Simplify

3. Subtract x from both sided of the equation

4. Simplify

Therefore, x = 10

Hope this helps :)

Answer:

=10

Add 4

to both sides of the equation 2−4=+6

2x-4=x+6 2−4+4=+6+4

Work out the percentage change when a price of £10 is increased to £14.​

Answers

Answer:

40%

Step-by-step explanation:

14-10 = 4, which is a 4 euro increase.

4/10 = 40%

Or we can see that 14/10 = 1.4, or 140%, which is a 40% increase

I NEED HELP ASAP IT'S DUE IN 40 MINUTES!!! I'LL GIVE BRAINLIEST!!!

Answers

Answer:

Transversal

Step-by-step explanation:

Could you guys help me again?

Answers

Answer:

1. n power of 25

2.x power of 5

You are shopping for school supplies. There is a sign at the front of the store advertising that you can either buy 4 binders and 4 notebooks for $17.00, or you can buy 2 binders and 6 notebooks for $15.50. Assume that the prices of binders and notebooks are constant. You have $30 total.

I. 6 binders and 8 notebooks

II. 8 binders and 6 notebooks

III. 12 binders

Which of the following combinations can you afford?
A. I only
B. I and II
C. I and III
B. II and III

Answers

Answer:

A) I only

Step-by-step explanation:

2x²+30y-3y²+4xy-14-x


Option 1,2,3 or 4?

Answers

there’s no alike terms so it would be option 3

If an author can type 2500 words in 5 minutes, how many words can he type in 210 minutes?

Answers

Answer:

105,000

Step-by-step explanation:

2500/5 gives you 500 x 210 =105,000

what is the value of u

Answers

Answer:

I think the value of u is 74.

Jordan is running sprints across a football field. He runs 30 yards in 6 seconds. At what
rate is Jordan running in yards per second?

Answers

Answer:

= 5 yards per second

Step-by-step explanation:

Have A Wonderful Day !!

Two tour groups are visiting an aquarium. There are 20 children in one group and 22 children in the other. Along with the 2 group leaders, there are 5 additional adults between the two groups. If the cost per child is $9.00 and the total for both groups is $490, what is the cost per adult?

Answers

Answer:

The cost per adult is $16.

Step-by-step explanation:

Given that:

Total number of children = 20+22 = 42 children

Total number of adults = 2 + 5 = 7 adults

Total cost for both groups = $490

Cost per child = $9.00

Cost of children ticket = 9.00*42 = $378

Cost of adult tickets = 490-378 = $112

This is the cost for 7 adult tickets.

Cost per ticket = [tex]\frac{112}{7}[/tex] = $16

Hence,

The cost per adult is $16.

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