Question

A quadratic polynomial 2x^2-mx+n has alpha and beta as two zeroes evaluate alpha square+beta square

Answer 1

Solution:-

2x^2 -mx+n ..........(1)


$\alpha + \beta = \frac{m}{2} \\ \alpha \beta = \frac{n}{2} \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ { \alpha }^{2} + { \beta }^{2} = \frac{ {m}^{2} }{4} - \frac{n}{2} \\ ({ \alpha }^{2} + { \beta }^{2} = \frac{ {m}^{2} + 4n}{4} )ans$