Question

What us the value of the discriminant of the quadratic equation -2^2=-8x+8 and what does its value mean about the number of a real number solutions the equation has

Answer 1

ANSWER

The discriminant is zero.

The given equation has one real root.

EXPLANATION

The given quadratic equation is:

$- 2 {x}^{2} = - 8x + 8$

We rewrite this in the form;

$a {x}^{2} + bx + c = 0$

$- 2 {x}^{2} + 8x - 8 = 0$

This means that,

a=-2, b= 8, c=-8

The discriminant is given by;

D=b² - 4ac

That is:

$D = {8}^{2} - 4( - 2)( - 8)$

$D = 64 - 64 = 0$

Therefore the discriminant is zero.

This tells us that the quadratic equation has one real root.

In order words, the given quadratic equation has a repeated real root.