Question

# If a and B are the zeroes of the quadratic polynomial f(x) = 2x2 - 5x + 7, find a polynomial whose zeroes are 2a+33 and 3a + 2B.

Solution

Since, a and ß are zeroes of polynomial f(x)=2x2 - 5x+7.
So, a+B=-(-5= and aß =
Let S and P denote respectively the sum and product of
zeroes of the required polynomial. Then, polynomial is
p(x)=k(x2 - Sx+P)