Question

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.

Answer 1

The correct option 3.

Explanation:

The given equation is

`-2x^2-3x+8=0`

The discriminant formula is

`D=b^2-4ac`

The value of discriminant for the given quadratic equation is

`D=(-3)^2-4(-2)(8)`

`D=9+64`

`D=73`

Therefore the value of the discriminant is 73.

The number of real solution depends on the value of discriminant.

1. If D=0, then the quadratic equation has one real solution.

2. If D>0, then the quadratic equation has two real solutions.

3. If D<0, then the quadratic equation has not real solutions.

Since the value of discriminant is greater than 0, therefore the equation has two real solutions.

Option 3 is correct.

Answer 2

Rewrite the equation:

-2x^2 - 3x + 8 = 0

2x^2 + 3x -8 =0

Where a=2, b=3 and c=-8

Then b^2 - 4ac = 3^2 - 4(2)(-8) = 9 + 64 = 73

A positive discriminant implies that the equation has two different real solutions.

Answer: the discriminant is 73, so the equation has 2 real solution