Multiple choice

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

  1. 0

  2. 1

  3. 2

  4. None of these
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A Correct answer
Explanation

For roots to be negatives of each other, the sum of roots must be zero. In ax^2 + bx + c = 0, sum of roots = -b/a. Here, -(-8m)/9 = 0, so 8m = 0, which means m = 0.

AI explanation

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by -b/a. If the roots are negatives of each other, their sum must be zero, meaning -b/a = 0 and thus b = 0. In the equation 9x^2 - 8mx - 9 = 0, the coefficient of x is -8m; setting this equal to zero gives -8m = 0, so m = 0.

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