Question

Determine the nature of the roots: 4x^2 + 32x + 64 = 0

a. no real solutions
b. a unique real solution
c. two distinct real solutions
d. cannot be determined

Answer 1

Answer: B a unique real solution

Explanation:

Edge2021

Answer 2

b. a unique real solution

Explanation:

A quadratic equation ax² + bx + c = 0 ,

Has two distinct real roots,

If discriminant,
`D=b^2 - 4ac > 1`

Has two equal real roots,

If D = 0,

Has two imaginary roots or no real roots,

if D < 1,

Here. the given qudratic equation,

`4x^2 + 32x + 64=0`

By comparing,

a = 4, b = 32, c = 64,

`\implies D = 32^2 - 4* 4* 64 = 1024 - 1024 = 0`

Hence, the equation has two equal real roots or a unique real solution.

i.e. OPTION 'b' is correct.