if a and b are the roots of the quadratic equationb ax^2 +bx +c =0 ,express (alpha-2beta)(2alpha-beta) in term if a,b,c . deduce the condition that one root of the equation is twice the other roots.

answer provided :2b^2 = 9ac, (2b^2-9ac)/a^2

2)if,a,b,c is subset of real number, with a is not equal to zero, and the roots of the quadratic equation ax^2+bx+c = 0 are real , show that the roots of ay^2 - (b^2-2ac)y + c^2 = 0 are also real. if the roots of quadratic equation ax^2 + bx +c = 0 states the value of alpha + beta and alpha Xbeta in terms of a,b,c . hence find the roots of the second equation in terms of a and b.

answer provided -b/a,c/a, alpha^2,beta^2