The quadratic equation whose roots are the arithmetic mean and the harmonic mean of the roots of the equation x 2 + 7 x - 1 = 0 is

Step-by-step solution

Let, α , β are the roots of the equation x 2 + 7 x - 1 = 0 ⇒ α + β = - 7 , α β = - 1 ⇒ A = α + β 2 = - 7 2 and H = 2 α β α + β = 2 - 1 - 7 = 2 7 . Now, equation whose roots are A and H is x 2 - A + H x + A H = 0 ⇒ x 2 - x - 7 2 + 2 7 + - 7 2 2 7 = 0 ⇒ x 2 + 45 14 x - 1 = 0 ⇒ 14 x 2 + 45 x - 14 = 0