Question

if alpha and beta are the zeros of the polynomial x is= 2X square + 5 x + k the equation relation alpha square +beta square + alpha beta is = 21 /
4 find the value of k​

Answer 1

Given:

★ A polynomial 2x²+5x+k .

★a²+ß² = 21/4

To Find:

★The value of k.

Concept Used:

★We will use some formulae realted to "quadratic polynomial".

Answer:

We have

Let p(x) = 2x²+5x+k .

w.r t Standard form ax²+bx+c ,

• a=2
• b=5 &
• c = k .

Now,we know,

If a & ß are zeroes then,

1. a +ß =-b/a
2. aß =c/a

so,

=> a² + ß² =²¹/4

=> a² + ß² + 2aß - 2aß =²¹/4

=>(a + ß )² =²¹/4+2aß

=>(-5/2)² = 21/4+2×k/2.

=> 25/4 =21/4+ k .

=>k = 25/4-21/4

=>k =4/4

.°. k = 1 .