If $3$ and $-6$ as the sum and product of its zeros respectively, then write the quadratic polynomial $f( x)$.

Given: $3$ and $-6$ as the sum and product of its zeros respectively.

To do: To write the quadratic polynomial $f( x)$.

Solution:

Let $\alpha$ and $\beta$ be the zeros of the quadratic polynomial, then 

$( \alpha+\beta)=3$

$\alpha\beta=-6$

The required polynomial will be

$f( x)=x^2-( \alpha+\beta)x+\alpha\beta$

$f( x)=x^2-3x-6$

Updated on: 10-Oct-2022

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