If α, β are the roots of the equation x2-2x-a2+1 = 0 and γ, δ are the roots of the equation x2-2(a+1)x+a(a-1)=0 such that α, β belongs to (γ,δ) , then find the values of ‘a’.
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3 Answers
62If alpha and beta are roots of this equation and alpha and beta should lie in between..
note that at any point between gamma and delta, value of the 2nd ffunction is negative
Hence we have f(α)<0 and f(β)<0
Which gives β2-2(a+1)β+a(a-1)<0 (same with alpha)
Moreover, β2-2β-a2+1=0 (same with alpha)
So, subtracting the two equations, we get
-2aβ+2a2-a-1<0
-2aα+2a2-a-1<0
so we want these two to be true..
Can you figure the next steps?
