Which describes the number and type of roots of the equation 4x^3-6x^2+15x+2=0?

a. 1 positive, 2 negative

b. 2 positive, 1 negative

c. 3 negative

d. 3 positive

Answer: Non of the option.

Step-by-step explanation:

The given equation is

4x^3 - 6x^2 + 15x + 2 = 0

Let's test 1, if it's one of the root. I. e

If x = 1

4 - 6 + 15 + 2 = 15

Positive 1 is not a root to the equation

If x = - 1

-4 - 6 - 15 + 2 = - 23

Negative 1 is not a root

If x = 2

4x8 - 6*4 + 15*4 + 2

32 - 24 + 30 + 2 = 40

Positive 2 is not a root

If x = - 2

4 * (-8) - 6*4 - 15*2 + 2

-32 - 24 - 30 + 2 = - 84

Negative 2 is not a root

If x = 3

4*27 - 6*9 + 15*3 + 2

108 - 54 + 45 + 2 = 101

Since non of them tend to zero, non of the option is a root of the equation