Question

If $\alpha$ and $\beta$ are the zeroes of a quadratic polynomial such that $\alpha +\beta =21$ and $\alpha -\beta =5$, then the polynomial is

• A. $x^2-21x+105$
• B. $x^2-21x+104$
• C. $x^2-21x+84$
• D. None of these

Answer 1

The correct option is B $x^2-21x+104$

$\text{If S and P be the sum and product of zeroes of quadratic equation, then quadratic Polynomial is given by}$
$x^2-Sx+P$
$\text{Now, given}S=\alpha +\beta =21$ $...\left(i\right)$
$\text{and}\alpha -\beta =5$
$\text{on adding, we get}$
$2\alpha =26\Rightarrow \alpha =13$
$\text{from (i)}\beta =8$
$\therefore P=\alpha \beta =104$
$\therefore \text{The required polynomial is}$
$x^2-21x+104$
Option B is correct.