Question

If a and b are the zeros of the quadratic polynomial $f\left(x\right)=6x^2+x-2$, find the value of $\frac{a}{b}+\frac{b}{a}$.

• A. $\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $\frac{5}{2}$
• D. $-\frac{25}{12}$

Answer 1

Answer: (D)

$-\frac{25}{12}$

$f\left(x\right)=6x^2+x-2$

a,b are its zero's / roots.

$a+b=\frac{-1}{6},ab=\frac{-2}{6}=-1/3$

$\frac{a}{b}+\frac{b}{a}=\frac{a^2+b^2}{ab}=\frac{(a+b{)}^2-2ab}{ab}$

$=\frac{(-1/6{)}^2-2(-1/3)}{(-1/3)}=\frac{\frac{1}{36}+\frac{2}{3}}{-1/3}$

$=-(\frac{1}{12}+2)=\frac{-25}{12}$