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?

The discriminant is equal to −16, which means the equation has no real number solutions.
The discriminant is equal to −16, which means the equation has two real number solutions.
The discriminant is equal to 24, which means the equation has no real number solutions.
The discriminant is equal to 24, which means the equation has two real number solutions.

Answer 1

-The equation is actually

5x^2 -2x+1=0;

-The discriminant is b^2 -4ac=4-4•5•1=4-20=-16

-this means that the equation has no real number solutions

Answer 2

The discriminant is equal to −16, which means the equation has no real number solutions.

Explanation:

`\text{Given the quadratic equation }-1=5x^2-2x`

we have to find the number of real number solutions the equation has.

The equation is

`5x^2-2x+1=0`

`\text{Comparing above equation }ax^2+bx+c=0`

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

To find number of real solutions we have to find the discriminant

`D=b^2-4ac`

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

`D=4-20=-16`

The value of discriminant is -16<0

Hence, the equation has no real roots.

Hence, option 1 is correct