Question

If alpha and beta are the zeros of the quadratic equation f(x)= ax^+bx+c,then evaluate alpha square/beta square +beta square/alpha square

Answer 1

Given quadratic polynomial is ax2 + bx + c
Given α, β are the zeroes of the given polynomial
α + β = ( – b/a)
αβ = (c/a)


Answer 2

as alpha and beta are roots of the quadratic eqn=> alpha + beta = -b/a and (alpha)(beta) = c/a
now alpha^2/beta^2 + beta^2/alpha^2 = (alpha^4 + beta^4)/alpha^2beta^2
= ((alpha^2 + beta^2)^2 - 2alpha^2beta^2)/(alpha× beta)^2
= (((alpha + beta)^2 - 2alpha×beta))^2 - 2(alpha×beta)^2)/(c/a)^2
= (( b^2/a^2 - 2c/a)^2 - 2c^2/a^2)/c^2/a^2
= (b^4/a^4 +4c^2/a^2 - 4b^2c/a^3 - 2c^2/a^2)/(c^2/a^2)
= (b^4/a^4 + 2c^2/a^2 - 4b^2c/a^3)/(c^2/a^2)