Question

If alpha and beta are the zeroes of the quadratic polynomial p(x)=ax2+bx+c then evaluate alpha^2/beta + beta^2/alpha

Answer 1

Step-by-step explanation:

a2/b + b2/a

by taking lcm we get

a3/ab+b3/ab.............(1)

as we know (a+b)^3= a3+b3+3ab(a+b)

therefore, a3 + b3 = (a+b)^3 - 3ab(a + b)

put this in eq. 1 we get

(a + b)^3 - 3ab (a + b)/ab

now we know a+b = -b/a

ab = c/a

then ,

-b3/a3 - 3c/a (-b/a)/c/a