Question

If p and q are the zeroes of the polynomial 2x^2+5x+k, find the value of k such that (p+q)^2-pq=24 accordingtoclass10th

Answer 1

$from \: \: the \: \: polynomial \\ p + q = \frac{ - 5}{2} . \: \: \: pq = \frac{k}{2} \\ {(p + q)}^{2} - pq = 24 \\ {( \frac{ - 5}{2}) }^{2} - \frac{k}{2} = 24 \\ 25 - 2k = 96 \\ k = \frac{ - 71}{2}$