Question

Find the value of $\frac{a}{b}+\frac{b}{a}$, if $a$ and $b$ are the roots of the quadratic equation $x^2+8x+4=0?$

• A. $14$
• B. $15$
• C. $24$
• D. $26$

Answer 1

The correct option is A $14$

$\frac{a}{b}+\frac{b}{a}$ = $\frac{a^2+b^2}{ab}$
= $\frac{(a^2+b^2+a+b)}{ab}$
= $\frac{\left[\right(a+b{)}^2-2ab]}{ab}$
= $a+b=\frac{-8}{1}=-8$
= $ab=\frac{4}{1}=4$
Hence $\frac{a}{b}+\frac{b}{a}$ = $\frac{\left[\right(-8{)}^2-2\left(4\right)]}{4}$
= $\frac{56}{4}=14$.