Question

If one zero of the polynomial 5z^2+13z-p is reciprocal of the other , then find p​

Answer 1

Step-by-step explanation:

$\: \: \: 5 {z}^{2} + 13z - p = 0 \\ = > \alpha . \beta = \frac{c}{a} \\ = > \alpha . \beta = \frac{ - p}{5} .........(eq \: no \: 1)\\ given\: that\: one \: zero \: of \: reciprocal \: \\ \: \: \: \: \: \: \: \: \: there \: fore \: \alpha . \beta = 1..........(eq \: no \: 2) \\ let \: compared \: eq \: no \: 1 \: and \: 2 \\ = > 1 = \frac{ - p}{5} \\ = > - p = 5 \\ = > p = - 5$