SOLUTION: If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square
Question 1207562: If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square
Instead of alpha and beta i will use p& q respectively
ax^2 + bx + c =0
p+q = -b/a and pq = c/a
(p+q)^2 = b^2/a^2
we have to find equation with roots p^2 and q^2
p^2+q^2 = (p+q)^2-2pq (from identity)
substitute (p+q)^2 and pq
sum of roots
p^2+q^2 = b^2/a^2-2(c/a)
product of roots
p2q^2= (pq)^2 = c^2/a^2
The general form of a quadratic equation is x^2-(sum of roots)x+(product of roots)=0
