Question

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★ STANDARD QUESTION 84 ★

The answer with highest efficiency will get marked THE Brainliest , And will be offered an special invitation card

Question is -

For what values of " m " will the equation
$\frac{x {}^{2} - bx }{ax - c} = \frac{m - 1}{m + 1}$
have roots equal in magnitude but opposite in sign ?



This question needs a perfect answer ; and it doesn't support lazy ones ! Take care

Answer 1

(m+1)(x² - bx) = (m-1)(ax-c)               (Cross - multiplication)

=>(m+1)x² - (m+1)bx - (m-1)ax + (m-1)c = 0
=>(m+1)x² - (mb + b + ma - a)x + (m-1)c = 0.

As per the conditions, the sum of roots is 0 setting the coefficient of x as 0.

=> m(a+b) + (b-a) = 0
=> m = (a-b)/(a+b).

There could be silly mistakes regarding sign, so just check it yourself. But I think it's okay.

Answer 2

This is the value of m.