Question

If alpha and bita are the zeroes of polynomial x square - 5x+k such that alpha - bita=1.find the value of k.

Answer 1

We have
${x}^{2} - 5x + k \\ \alpha - \beta = 1 \\ \alpha + \beta = \frac{ - ( - 5)}{1} = 5 \\ \alpha = 3 \\ \beta = 2$
Now we know that
$\alpha \beta = \frac{k}{1} \\ k = 3 \times 2 = 6$
^_^