Show that the polynomial `f(x)= x^2 + px + q` has a repeated zero, if `4p^2 + 27q^2 = 0`

Show f(x)= x^3+px+q =0 has a repeated root if 4p^3+27q^2 =0

If alpha and beta are zeros of polynomial f(x) = x^(2) + px + q , form a polynomial whose zeros are (alpha + beta)^(2) are (alpha - beta)^(2) .

If p,q are zeroes of polynomial f(x)= 2x^(2)-7x+3 find the value of p^(2)+q^(2)

If alpha and beta are the zeros of the polynomial f(x) = x^(2) + px + q , then a polynomial having 1/(alpha) and 1/beta as its zeros is …………..

If the zeroes of the polynomial x^(2)+px+q are double in the value of the zeroes of 2x^(2)-9x+4 , find the values of p and q.

If alpha and beta are the zeros of the polynomial f(x)=x^(2)+px+q, form a polynomial whose zeros are (alpha+beta)^(2) and (alpha-beta)^(2)

If alpha and beta are zeros of the quadratic polynomial f(x) = x^(2) - px + q , prove that (alpha^(2))/(beta^(2)) +(beta^(2))/(alpha^(2)) = (p^(4))/(q^(2)) - (4p^(2))/(q) + 2 .

If alpha and beta are the zeros of the polynomial p(x) = x^(2) - px + q , then find the value of (1)/(alpha)+(1)/(beta)

Verify that (i) 4 is a zero of the polynomial , p (x) = x -4. (ii) -3 is a zero of the polynomial , q (x) = x+3. (iii) (2)/(5) is a zero of the polynomial , f (x) =2 - 5x. (iv) (-1)/(2) is a zero of the polynomial , g (y) = 2y +1.

If the zeroes of the polynomial x^2+px+q are double the value to the zeroes 2x^2-5x-3 find the value of p and q