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?

the discriminant is equal to 0, which means the equation has no real number solutions.
the discriminant is equal to 0, which means the equation has one real number solution.
the discriminant is equal to 128, which means the equation has no real number solutions.
the discriminant is equal to 128, which means the equation has two real number solutions.

Answer : The discriminant is equal to 0, which means the equation has one real number solution.

The given quadratic equation is  

To find discriminant we use formula D=

When D >0, the equation has two real solutions.

when D <0, the equation has two complex solutions

When D=0, the equation has one real solution.

First we write the equation in the form of

 , a= -2, b=8, c=-8

Now we need to calculate D to find the number of solutions.

Discriminant D= =0

D=0 so, the equation has one real solution.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

the answer is 1/4

step-by-step explanation: