Question

If alpha and beta are the zeros of the polynomial 2x^2 + 5x + k . satisfying the relation alpha square + beta square + alpha beta = 21/4 . find the value of kshould be in detailed

Answer 1

SOLUTION :-

=>that if alpha and beta are the zeros of 2x²+5x+k satisfying the relation,

=> α²+β² + α.β=21/4.

We have to find the value of k,

=>Comparing 2x²+5x+k with standard quadratic polynomial of form ax²+bx+c , we get

=>a=2, b=5 and c=k

=>Sum of roots = α+β = -b/a = -5/2

=>Product of roots= α.β = c/a = k/2

=>α²+ β²+ α.β = 21/4

=>(α + β)² - α . β = 21/4

=>(-5/2)²-k/2 = 21/4

=>25/4 - k/2 = 21/4

=>25/4 - 21/4 = k/2

=> k=2

The value of k is 2.

Answer 2

SOLUTION :-

=>that if alpha and beta are the zeros of 2x²+5x+k satisfying the relation,

=> α²+β² + α.β=21/4.

we have to find the value of k,

=>Comparing 2x^2+5x+k with standard quadratic polynomial of form ax^2+bx+c , we get

=>a=2, b=5 and c=k

=>Sum of roots=α+β=-b/a= -5/2

=>Product of roots= α.β = c/a =k/2

=>α²+ β²+ α.β = 21/4

=>(α + β)² - α . β =21/4

=>(-5/2)²-k/2=21/4

=>25/4 - k/2=21/4

=>25/4 - 21/4=k/2

=> k=2

The value of k is 2.