if a and b are zeros of polynomialf(x)=x2-3x-2,find the quadratic polynomial whose zeros are 1/2a+b and 1/2b+a

It is given that a and b are zeros of polynomial f(x)=x²-3x-2.

Therefore, a+b=3

ab=-2

Now, the zeroes of the required quadratic polynomial are 

Sum of roots = Product of roots =

 

Now, the required quadratic polynomial is given by:

x² - (Sum of roots)x + (Product of roots)

Now, substitute the values