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What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?

The discriminant is −55, so the equation has 2 real solutions.
The discriminant is −55, so the equation has no real solutions.
The discriminant is 73, so the equation has 2 real solutions.
The discriminant is 73, so the equation has no real solutions.

Respuesta :

ghanami
hello:
 −2x² − 3x + 8
 delta = (-3)²-4(-2)(8) =9+64 = 73 ... (delta) > 0
The discriminant is 73, so the equation has 2 real solutions

Answer:

C. The discriminant is 73, so the equation has 2 real solutions.

Step-by-step explanation:

We have been given an equation [tex]-2x^2-3x+8=0[/tex]. We are asked to determine the number of real solutions for our given equation using discriminant formula.

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

D = Discriminant,

b = Coefficient of x or middle term.

a = Leading coefficient,

c = constant.

When [tex]D=0[/tex], the equation has two real and equal zeros.

When [tex]D>0[/tex], the equation has two real and distinct zeros.

When [tex]D<0[/tex], the equation has no real zeros.

Upon substituting our given values in above formula we will get,

[tex]D=(-3)^2-4*-2*8[/tex]

[tex]D=9+8*8[/tex]

[tex]D=9+64[/tex]

[tex]D=73[/tex]

Since the value of discriminant is 73 that is greater than 0, therefore, the equation has two real zeros and option C is the correct choice.

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