Question

what is the value of the discriminant of the quadratic equation -2x^2 = -8x + 8, and what does its value mean about the number of real number solutions the equation has? the discriminant is equal to 0, which means the equation has no real number solutions. the discriminant is equal to 0, which means the equation has one real number solution. the discriminant is equal to 128, which means the equation has no real number solutions. the discriminant is equal to 128, which means the equation has two real number solutions.

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $-2x^{2}=-8x + 8$ as $-2x^{2}+8x - 8=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a=-2$, $b = 8$, and $c=-8$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a=-2$, $b = 8$, and $c=-8$ into the formula: $\Delta=(8)^{2}-4\times(-2)\times(-8)=64 - 64=0$.

Step3: Determine the number of real - number solutions

If $\Delta = 0$, the quadratic equation has one real - number solution.

Answer:

The discriminant is equal to 0, which means the equation has one real number solution.