If a and B are the zoros of the quadratic polynomial p(x)=4x^2 - 5x-1, find value of a^2B + aB^2 .
Solution
SINCE a and B are the roots of the polynomial: 4x^2-5x-1
Sum of the roots a+B =5/4
Product of the roots aB=-1/4
HENCE
a^2B+aB^2=aB(a+B)=5/4(-1/4)=-5/16
Concept:Relationship Between Zeroes and coefficients of a Polynomial