Describe the roots of the equation shown below.
64x^2 - 16x + 1=0

a. there are two complex roots
b. there is one real, double root
c. there are two real, irrational roots
d. there are two real, rational roots

B. There is one real, double root

Step-by-step explanation:

For ax² + bx + c = 0, the discriminant is b² − 4ac.

If the discriminant is positive and a perfect square, there are two real, rational roots.

If the discriminant is positive and not a perfect square, there are two real, irrational roots.

If the discriminant is 0, there is one real, double root.

If the discriminant is negative, there are two complex roots.

Here, a = 64, b = -16, and c = 1.

b² − 4ac

= (-16)² − 4(64)(1)

= 0

The discriminant is 0.  Therefore, there is one real, double root

step-by-step explanation:

quartic functions has x = –1 and x = –2 as its only two real zeroes:

f(x) = a(x+2)(x+1)   a: real number