Multiple choice

Mani was asked to form a quadratic equation such that the square of the difference of the roots when multiplied by the sum of the roots gives an answer which is 288 times the difference of roots. If the roots are integers, how many quadratic equations are possible?

  1. 6

  2. 12

  3. 18

  4. 24

  5. Data inadequate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let roots be alpha, beta. (alpha-beta)^2 * (alpha+beta) = 288 * (alpha-beta). (alpha-beta)(alpha+beta) = 288. alpha^2 - beta^2 = 288. Since alpha, beta are integers, we look for factors of 288. There are 24 pairs of integers satisfying this.

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