The value of a for which the eq. (1-a)x^(2) +2ax -1 =0 has roots belonging to interval (0,1)

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Solution

Dear student
There is some mistake in your equation.
$L e t f (x) = (1 - a^{2}) x^{2} + 2 a x - 1 = 0 T h e n . f (0) = - 1 a n d f (1) = (1 - a^{2}) + 2 a - 1 < 0 o r 1 - a^{2} + 2 a - 1 < 0 o r a^{2} - 2 a > 0 a < 0, d o e s n o t s a t i s f y t h e r e q u i r e m e n t t h a t b o t h t h e r o o t s a r e p o s i t i v e . H e n c e, a > 2 .$

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