Question

if alpha and beta are zero's of the polynomial f(x) = 2x^2+5x+k if alpha^2 + beta^2 + alpha beta=24 find k​

Answer 1

f( x) = 2x²+ 5x+ k

Then, alpha +beta =

- coeff.of x/ coeff of x²= - 5/2

And, alpha beta =

constant  term  / coeff. of x²

= k/2

Therefore , alpha²+ beta²

= ( alpha+ beta) ²

               - 2 alpha beta= 24

(-5/2 )²- 2× k/2=24

= 25/ 4 - k =24

= 25- 4k/ 4 = 24

= 25 - 4k = 24×4

= 25- 4k = 96

= -4k = 96- 25

= -4k = 71

k= 71/-4

 = - 71/ 4