Question

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

Answer 1

Answer:

b. a unique real solution

Step-by-step 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,

$\implies D = 32^2 - 4\times 4\times 64 = 1024 - 1024 = 0$

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

i.e. OPTION 'b' is correct.

Answer 2

Answer:

A unique real solution

Step-by-step explanation: