Let a, b R, a ≠ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root α, which is also a root of the equation, x² – 2bx – 10 = 0. If β is the other root of this equation, then α ² + β ² is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2020 Mathematics question

JEE Main 2020 · 9 Jan, Evening shift · Q5056

JEE Main 20209 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let a, b

\in

R, a

\ne

0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root

\alpha

, which is also a root of the equation, x² – 2bx – 10 = 0. If

\beta

is the other root of this equation, then

\alpha

² +

\beta

² is equal to :