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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?

Respuesta :

Answer:

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

Step-by-step explanation:

Given quadratic equation is [tex]-2x^2=-8x+8[/tex]

To find : The value of the discriminant .

[tex]-2x^2=-8x+8[/tex]

[tex]-2x^2+8x-8=0[/tex]

Multiplying by "-" on both sides

[tex]2x^2-8x+8=0[/tex]

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

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

By Discriminant formula:

[tex]D = b^2-4ac[/tex]

Substituting the values in the formula

[tex]D=(-8)^2-4(2)(8)[/tex]

[tex]=8^2-64[/tex]

[tex]=64-64[/tex]

[tex]=0[/tex]

∴ 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.

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