Question

If $\alpha$ and $\beta$ are the zeros of the polynomial $p\left(x\right)=x^2+x-12$, then $\frac{1}{\alpha }+\frac{1}{\beta }=..........$

Answer 1

We have,

Polynomial $p\left(x\right)=x^2+x-12$

Roots are given $\alpha$ and $\beta$

Then, $Sumofzeros=-\frac{cofficentsofx}{cofficentsof{x}^2}$

$\alpha +\beta =-\frac{1}{1}=-1$

$Productofzeros=\frac{\mathrm{constant}}{cofficentof{x}^2}$

$\alpha \times \beta =\frac{-12}{1}=-12$

Then,

$\frac{1}{\alpha }+\frac{1}{\beta }$

$=\frac{\alpha +\beta }{\alpha \beta }$

$=\frac{-1}{-12}$

$=\frac{1}{12}$

Hence, this is the answer.