Question

If $a,b$ are the zeroes of the polynomial $x^2-7x+6$ then, $\frac{1}{a}+\frac{1}{b}$ is

• A. $-1$
• B. $\frac{7}{6}$
• C. $7$
• D. $-6$

Answer 1

The correct option is B $\frac{7}{6}$

$\text{Given, a,b are the zeroes of the polynomial}$ $x^2-7x+6$

$\Rightarrow a+b=7$ {property of the roots of the quadratic equation, sum of roots $=\frac{-b}{a}$}

$\Rightarrow ab=6$ {property of the roots of the quadratic equation, product of the roots $=\frac{c}{a}$}

Now, $\frac{1}{a}+\frac{1}{b}=\frac{b+a}{ab}=\frac{7}{6}$

Option B is correct.