6.A quadratic polynomial,whose zeroes are 2 and -3

A quadratic polynomial, whose zeroes are -3 and 4 , is

Find a quadratic polynomial whose zeroes are -2 and 5. Hence, verify the relation between zeroes and coefficients of the polynomial.

If alpha,beta are zeroes of the polynomial x^2-2x-15 , then form a quadratic polynomial whose zeroes are (2alpha) and (2beta) .

Find the quadratic polynomial whose zeroes are -(1)/(3) and (2)/(5) . Verify the relation between coefficients and zeroes of the polynomial.

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2-3x-2 , find a quadratic polynomial whose zeros are 1/(2alpha+beta) and 1/(2beta+alpha) .

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2-1 , find a quadratic polynomial whose zeros are (2alpha)/beta and (2beta)/alpha .

If alpha and beta are the zeros of the quadratic polynomial f(x)=3x^2-4x+1 , find a quadratic polynomial whose zeros are (alpha^2)/beta and (beta^2)/alpha .

Find a quadratic polynomial whose zeros are reciprocals of the zero of the polynomial f(x)=a x^2+b x+c , a!=0 ,c!=0.

Write a quadratic polynomial, sum of whose zeros is 2sqrt(3) and their product is 2.

Write a quadratic polynomial, sum of whose zeros is 2sqrt(3) and their product is 2.