Question

If alpha and beta are the zeroes of the polynomial f (X)=2x^2+5x+k, satisfying the relation alpha^2+ beta^2+alpha* beta=21/4. Find the value of k

Answer 1

Answer:

k=2

Step-by-step explanation:

alpha^2+beta^2+alpha.beta=21/4

(alpha+beta)^2-2alpha.beta+alpha.beta=21/4

(-b/a)^2-(c/a)=21/4

(-5/2)^2-(k/2)=21/4

25/4-k/2=21/4

25-2k/4=21/4

25-2k=21

k=2