Question

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

Answer 1

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).

Answer 2

Option D is the correct answer.

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.