Let a, b R be such that the equation a x² - 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x² - 2bx + 21 = 0, then α ² + β ² is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Evening shift · Q5057

JEE Main 202225 Jun, Evening shiftMathematicsEasyComplex Numbers and Quadratic Equations264× since 2002

Let a, b

\in

R be such that the equation

a{x^2} - 2bx + 15 = 0

has a repeated root

\alpha

. If

\alpha

and

\beta

are the roots of the equation

{x^2} - 2bx + 21 = 0

, then

{\alpha ^2} + {\beta ^2}

is equal to :