Question

16. If a and Bare the zeros of the quadratic polynomial f(x) = x2 - 3x - 2, find a quadratic
polynomial whose zeros are 1/2α+β and 1/2β+α.​

Answer 1

Answer f(x) = x2-3x-2

therefore= a+b =3

ab=2

Now, 1/2a+b and1/2b+a

Sum of roots = 9/16

Product of roots =1/16

Now ,

x2- (sum of roots)x + (product of roots)

x2 - 9/16 +1/16

Step-by-step explanation: