Question

If alpha and beta are the zeros of the polynomial 25x2+25x+5, then find the value of 1/alpha2 +1/beta2

Answer 1

sum of roots alpha +beta= -coefficient of x÷coefficient of x^2

alpha +beta=-25÷25

=-1

product of roots alpha×beta= constant term÷coefficient of x^2

alpha×beta=1÷5

I/alpha^2 + 1/beta^2

alpha^2 +beta^2 ÷ alpha^2 ×beta ^2

=((alpha +beta)^2 -2×alpha×beta)÷ (alphaxbeta)^2

=(1-2÷5)÷4÷25

(3÷5)÷(4÷25)

=15÷4

Answer the reciprocal of square of the roots of the numbers is 15÷4