Question

$aandb$ are the zeroes of a quadratic polynomial $p\left(x\right)$, and $k$ is any constant. Then general form of polynomial is.

• A. $k{x}^2+(a+b)x+ab$
• B. $k{x}^2+k(a+b)x+kab$
• C. $k{x}^2-k(a+b)x+kab$

Answer 1

The correct option is C $k{x}^2-k(a+b)x+kab$

Given, '$a$' and '$b$' are the zeroes of the quadratic polynomial $p\left(x\right)$.
This polynomial should be equal to zero when $x=a$ or $x=b$.
$\therefore x-a,x-b$ are factors of $p\left(x\right)$.
$\Rightarrow p\left(x\right)=k(x-a)(x-b)p\left(x\right)=k{x}^2-k(a+b)x+kab$