Question

Find the discriminant of each of the equations below and state the number of solutions:

-4x²+2x+10=8

Answer 1

The discriminant of the quadratic equation -4x²+2x+2=0 is 36, which indicates that there are two distinct real solutions.

Step-by-step explanation:

The given equation is rearranged to a quadratic equation that equals 0:
-4x²+2x+10=8
By subtracting 8 from both sides, we get:
-4x²+2x+2=0
The discriminant of a quadratic equation of the form ax²+bx+c=0 is given by Δ=b²-4ac.

In this equation, a=-4, b=2, and c=2. Therefore, the discriminant is:
Δ=2²-4(-4)(2)
Calculating further:
Δ=4+32=36

Since the discriminant is positive (Δ>0), the quadratic equation has two distinct real solutions.