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Question

Find the value of 'm' so that the equation ${9 x}^{2} - 8 m x - 9 = 0$ has one root as the negative of the other.

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Solution

The correct option is B 0
Given equation is: $9 x^{2} - 8 m x - 9 = 0$
Comparing with standard equation $a x^{2} + b x + c = 0$ , we get
$a = 9, b = - 8 m, c = - 9$
Let $α, β$ be the roots
Then, $α + β = - \frac{b}{a} = \frac{8 m}{9}$
But, $α = - β$
Thus, $α + β = 0$
$\Rightarrow \frac{8 m}{9} = 0$
$\Rightarrow m = 0$

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