Question

Use the discriminant to determine the number of real-number solutions for the equation:

8x2 + 8x + 2 = 0
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions

Answer 1

Option A is correct one.


Explanation :
Δ of ax^2 +bx +c is b^2 -4ac
And if the Δ =0 then, we have one real root
And if Δ > 0 then the roots are real and distinct
And if Δ < 0 then there are no real roots

In above equation a =8, b = 8 and c = 2
Apply the discriminant now,
b^2 -4ac
(8)^2-(4)(8)(2)
64 - 64 =0

Here, the Δ = 0
So this equation has one solutions.

[Note: Δ is the symbol used to represent discriminant]

Answer 2

The discriminant is-

b^2-4ac=64-64=0

as the discriminant is 0, one solution will be -b/2a = -1/2

But still, we can't say that it has only one solution due to the nature of quadratic equations(It's tendency to have two solutions).
But we can say that both solutions are coincident.

Hence it has two solutions.

HOPE IT HELPED!!!☺