Question

What is the value of the discriminant of the quadratic equation −2x2 = −8x + 8, and what does its value mean about the number of real number solutions the equation has?

Answer 1

For this case we have the following quadratic equation:

`-2x ^ 2 = -8x + 8`

Rewriting we have:

`2x ^ 2-8x + 8 = 0`

This equation is of the form
`ax ^ 2 + bx + c = 0`

Where:

`a = 2\\b = -8\\c = 8`

The discriminant is given by:

`d = b ^ 2-4 (a) (c)\\d = (- 8) ^ 2-4 (2) (8)\\d = 64-64\\d = 0`

This means that the equation has two equal real roots.

Answer:

`d = 0`

The equation has two equal real roots.