Question

If alpha and beta are zeroes of quadratic polynomial 2x2+5x+k. find valye of k

Answer 1

$\alpha + \beta = \frac{ - b}{a} = \frac{ - 5}{2} \\ \alpha \beta = \frac{c}{a} = \frac{k}{2}$
using quadratic formula
$\alpha = \frac{ - 5 + \sqrt{25 - 8k} }{4} \\ \beta = \frac{ - 5 - \sqrt{25 - 8k} }{4} \\ \alpha \beta = \frac{( { - 5)}^{2} - ( { \sqrt{25 - 8k} )}^{2} }{16} = \frac{k}{2} \\ \frac{25 - 25 + 8k}{16} = \frac{k}{2} \\ \frac{k}{2} = \frac{k}{2}$
with this information only,value of k can't be find.you can check that I had applied few ways,but at last k cancels.please check the question