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Question

Let a, b  R,a0, such that the equation, ax22bx+5=0 has a repeated root α, which is also a root of the equation x22bx10=0. If β is the other root of this equation, then α2+β2 is equal to: 
  1. 24
  2. 25
  3. 26
  4. 28


Solution

The correct option is B 25
ax22bx+5=0 has both roots as α
 2α=2baα=ba
And α2=5a
b2=5a(a0)(1)          
 α+β=2b and αβ=10

β,α are the roots of x22bx10=0.
α=ba
b22ab210a2=0
5a10a210a2=0      ( Using (1))
a=14b2=54
α2=20,β2=5α2+β2=25

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