Question

If $\alpha$ and $\beta$ are two zeroes of the polynomial $x^2-7x+k$ where $\alpha -\beta =5$, find value of k.

Answer 1

If $\alpha$ and $\beta$ are two zeros of

$x^2-7x+k=0$

$\underset{–}{\begin{array}{c}\alpha -\beta =5\\ \alpha +\beta =7\end{array}}$

$2\alpha =12$

$\alpha =6$

$\therefore \beta =1$

$\therefore k=\alpha \beta =6$