Choose the best description of the roots of the equation 3x 2 - 4x + 5 = 0.

double root

real and rational roots

real and irrational roots

imaginary roots

Option D is the correct answer.

Step-by-step explanation:

Properties of roots of ax²+bx+c=0 are decided by discriminant b² - 4ac

If b² - 4ac > 0 real and distinctive roots

If b² - 4ac = 0 equal roots

If b² - 4ac < 0 imaginary roots

We have 3x²-4x+5=0

a = 3, b = - 4 and c = 5

b² - 4ac = (-4) ²-4 x 3 x 5 = 16 - 60 = - 44 < 0

So roots are imaginary.

Option D is the correct answer.

To see, we should use the quadratic formula:

(-b + / - sqrt (b - 4ac)) / 2a

We plug the values in:

( - (-4) + / - sqrt (-4 - 4 * 3 * 5)) / (2 * 3)

(4 + / - sqrt (-64)) / 6

But, we can't have a negative square root, so we use i for imaginary.

That means that we will have imaginary roots, so the answer is (D).