Question

IWhat 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

The value of the Discriminant is D=0 in the given quadratic equation .

The value of the discriminant D=0 mean that the number of real number solutions in the equation has double real roots

Explanation:

Given quadratic equation is
`-2x^2=-8x+8`

To find : The value of the discriminant .

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

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

Multiplying by "-" on both sides

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

Now comparing the above quadratic equation in the standard form of quadratic equation
`ax^2+bx +c = 0` we get.

The values of , a = 2, b= -8, and c = 8

By Discriminant formula:

`D = b^2-4ac`

Substituting the values in the formula

`D=(-8)^2-4(2)(8)`

`=8^2-64`

`=64-64`

`=0`

∴ D=0

We know that if the discriminant D= 0, it has double real roots.

∴ The value of the Discriminant is D=0 in the given quadratic equation

The value of the discriminant D=0 mean that the number of real number solutions in the equation has double real roots.