If a and B are the zeroes of a quadraticpolynomial x?+pat q, then find

1.	If a and B are the zeroes of a quadraticpolynomial x?+pat q, then find the value of(8 +2)x(& +2)
Answer» alpha and beta are zeroes of a quadratic polynomial x^2 + px + q,Then,alpha + beta = - palphabeta = q (alpha + beta)^2 = alpha^2 + beta^2 + 2alphabeta alpha^2 + beta^2 = p^2 - 2q Therefore,Value of (alpha/beta + 2)(beta/alpha + 2) = (alpha + 2 beta)(beta + 2 alpha)/alphabeta = (5alphabeta + 2(alpha^2 + beta^2)) /alpha*beta = 5q + 2(p^2 - 2q)/q

If a and B are the zeroes of a quadraticpolynomial x?+pat q, then find the value of(8 +2)x(& +2)

Answer»

alpha and beta are zeroes of a quadratic polynomial x^2 + px + q,Then,alpha + beta = - palpha*beta = q

(alpha + beta)^2 = alpha^2 + beta^2 + 2alpha*beta

alpha^2 + beta^2 = p^2 - 2q

Therefore,Value of (alpha/beta + 2)(beta/alpha + 2)

= (alpha + 2 beta)(beta + 2 alpha)/alpha*beta

= (5alpha*beta + 2(alpha^2 + beta^2)) /alpha*beta

= 5q + 2(p^2 - 2q)/q