Answer:
b. a unique real solution
Step-by-step explanation:
A quadratic equation ax² + bx + c = 0 ,
Has two distinct real roots,
If discriminant, [tex]D=b^2 - 4ac > 1[/tex]
Has two equal real roots,
If D = 0,
Has two imaginary roots or no real roots,
if D < 1,
Here. the given qudratic equation,
[tex]4x^2 + 32x + 64=0[/tex]
By comparing,
a = 4, b = 32, c = 64,
[tex]\implies D = 32^2 - 4\times 4\times 64 = 1024 - 1024 = 0[/tex]
Hence, the equation has two equal real roots or a unique real solution.
i.e. OPTION 'b' is correct.
