hence explain x²-8x+20 is always positive

Answer:

It is always positive because the discriminant is negative and therefore has no roots. This can also be interperted as the equation will always be above the x-axis on the parabola and therefore always be positive.

Step-by-step explanation:

The value of the quadratic expression (x - 4)² + 4 will be always positive.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient. Then the equation of the parabola will be given as,

y = a(x - h)² + k

The quadratic expression is given below.

⇒ x² - 8x + 20

Convert the expression into a vertex form, then we have

⇒ x² - 8x + 16 + 4

⇒ (x² - 2 · x · 4 + 4²) + 4

⇒ (x - 4)² + 4

Thus, the value of the expression (x - 4)² + 4 will be always positive.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

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