Question

Find the equation whose roots are less by 3, than those of 3x2
– 7x + 6 = 0.

Answer 1

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