Let a , b ∈ R be such that the equation a x 2 - 2 b x + 15 = 0 has repeated root α and if α and β are the roots of the equation x 2 - 2 b x + 21 = 0 , then α 2 + β 2 is equal to:

Step-by-step solution

Given a x 2 - 2 b x + 15 = 0         . . . i Has repeated roots So D = 0 4 b 2 - 4 × 15 × a = 0 ⇒ b 2 = 15 a       . . . ii Also given Now α will satisfy both quadratic a x 2 - 2 b x + 15 = 0   &   x 2 - 2 b x + 21 = 0   Putting the value we get   a α 2 - 2 b α + 15 = 0     α 2 - 2 b α + 21 = 0 -       +                 -         &#1