Question

if alpha and beta are the zeroes of polynomial 2x^2 -9x-7 than find the value of alpha^2 + beta^2​

Answer 1

Answer:

$\bf \alpha ^2+\beta ^2 =\frac{109}{4}$

Step-by-step explanation:

α,β are zeros of

p(x)=2x²-9x-7

Thus $\alpha +\beta =-\frac{-9}{2} =\frac92\\\\\alpha \beta =\frac{-7}{2} =-\frac72\\\\\therefore \alpha ^2+\beta ^2=(\alpha+ \beta )^2-2\alpha \beta \\\\=( \frac92)^2-2(-\frac{7}{2} )\\\\=\frac{81}{4} +7\\\\=\frac{81+28}{4} \\\\\bf =\frac{109}{4}$