Question

Options
A: 0
B: 1
C:2
D:3

Answer 1

B. 1

Explanation:

The given expression is ;

`f(x)=4x^3-13x^2+9x+2`

The graph intersected the x-axis at three points.

These are called the real roots.

Among these real roots are rational and irrational roots.

According to the rational roots theorem, the possible rational roots are;

`\pm(1)/(4) ,\pm(1)/(2) ,\pm1,\pm2`

Among these possible rational roots, only

`P(2)=4(2)^3-13(2)^2+9(2)+2`

`P(2)=32-52+18+2`

`P(2)=-2+2=0`

Hence the other two roots are irrational.