Question

find the equation whose roots are the squares of the roots of the equation x^3+3x^2-7x+6=0​

Answer 1

Answer:

Given equation is f(x) = x3 + 3x2 – 7x + 6 = 0 Required equation is f(√x) = 0 ⇒ x√x + 3x – 7√x + 6 = 0 ⇒ √x(x – 7) = – (3x + 6) Squaring on both sides, ⇒ x(x – 7)2 = (3x + 6)2 ⇒ x(x2 – 14x + 49) = 9x2 + 36 +36x ⇒ x3 – 14x2 + 49x – 9x2 – 36x – 36 = 0 i.e. x3 – 23x2 + 13x – 36 = 0