Question

If $\alpha \&\beta$ are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?

• A. $k\left[x^2-(\alpha +\beta )x+\alpha \beta \right]$
• B. $k{x}^2-(\alpha +\beta )x-\alpha \beta$
• C. $k{x}^2+(\alpha +\beta )x-\alpha \beta$
• D. $k^2{x}^2+k(\alpha +\beta )x+k\alpha \beta$

Answer 1

The correct option is A $k\left[x^2-(\alpha +\beta )x+\alpha \beta \right]$

Given, $\alpha \&\beta$ are the zeroes of the quadratic polynomial p(x).

This polynomial should be equal to zero when $x=\alpha$ or $x=\beta$.

$\Rightarrow x-\alpha ,x-\beta$ are factors of p(x).

$\Rightarrow p\left(x\right)=k(x-\alpha )(x-\beta )$

$\Rightarrow p\left(x\right)=k\left[x^2-(\alpha +\beta )x+\alpha \beta \right]$