Question

The quadratic polynomial whose product and sum of the zeroes are $1$ and $-12,$ respectively is :

• A. $x^2-x-12$
• B. $x^2-12x-1$
• C. $x^2+x-12$
• D. $x^2+12x+1$

Answer 1

The correct option is D $x^2+12x+1$

Given: Sum of zeroes $=-12$ and product of zeroes $=1$

We know,

$p\left(x\right)=x^2-\left(\text{sum of zeroes}\right)x+\left(\text{product of zeroes}\right)$

$\Rightarrow p\left(x\right)=x^2-(-12)x+1$

$\Rightarrow p\left(x\right)=x^2+12x+1$

is the required polynomial.