Question

What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?

Answer 1

First add one to both sides to make the left side 0. This makes the a value 5 theb value -2 and the c value 1. The discriminant is b squared -4ac. Plug it in to get (-2)^2-4(5). 4-10=-6. The resulting number is less than zero so there are no real number solutions.

Answer 2

discriminant of the quadratic equation is -16, The resulting number is less than zero so there are no real number solutions.

Explanation:

Given : he quadratic equation −1 = 5x² −2x.

To find : What is the value of the discriminant .

Solution : We have given that −1 = 5x² −2x.

−1 = 5x² −2x.

On adding by 1 both sides

0 = 5x² −2x +1

On switching sides

5x² −2x +1 = 0

Compare it standard form of quadratic equation ax² +bx +c = 0.

Here, a = 5, b= -2, c = 1

By Discriminant formula:

D =
`b^(2) -4ac`

Substituting the values

D =
`(-2)^(2) -4(5)(1)`.

D = 4 - 20

D = -16.

Therefore, discriminant of the quadratic equation is -16, The resulting number is less than zero so there are no real number solutions.