Answer:
B. 1
Step-by-step explanation:
The given expression is ;
[tex]f(x)=4x^3-13x^2+9x+2[/tex]
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;
[tex]\pm\frac{1}{4} ,\pm\frac{1}{2} ,\pm1,\pm2[/tex]
Among these possible rational roots, only
[tex]P(2)=4(2)^3-13(2)^2+9(2)+2[/tex]
[tex]P(2)=32-52+18+2[/tex]
[tex]P(2)=-2+2=0[/tex]
Hence the other two roots are irrational.
