Question

Let one root of the equation x^2 + lx + m = 0 is square of other root then

Answer 1

Let one root of the equation x^2 + lx + m = 0 is square of other root then

∛m and ∛m² are the roots of the equation.

• Let the roots be a and b.

• Then given b  = a^2.

In the quadratic equation given,

• We know sum of roots  =
• a + a^2 =  -l

• And product of roots =
• a.a^2 = a^3 = m

Therefore,

• a = ∛m

• a^2 = ∛m²

are the two roots of the given quadratic equation.