Multiple choice

If roots of equation $9 x ^ { 2 } - 6 x - ( 2 m + 1 ) = 0$ are reciprocal of each other then $m =?$

  1. $-5$
  2. $5$
  3. $-4$
  4. $4$
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A Correct answer
Explanation

When the roots of a quadratic equation ax^2 + bx + c = 0 are reciprocals of each other, their product is 1, which means c = a. Setting the constant term -(2m + 1) equal to the coefficient of x^2, which is 9, gives -(2m + 1) = 9, solving to m = -5.

AI explanation

For the roots of the quadratic equation 9x^2 - 6x - (2m + 1) = 0 to be reciprocals of each other, the product of the roots must equal 1. Using Vieta's formulas, the product of the roots is c/a, which is -(2m + 1)/9. Setting this equal to 1 gives -(2m + 1) = 9, so 2m + 1 = -9. Solving for m yields 2m = -10, which means m is -5.

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