Multiple choice

If one root of the equation $x^{2} - 12x + 3k = 0$ is square of the other, then k is

  1. 3

  2. 9

  3. 6

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let roots be a and a^2. Sum = a + a^2 = 12. Product = a^3 = 3k. From a + a^2 = 12, a^2 + a - 12 = 0, (a+4)(a-3) = 0. If a=3, a^3 = 27 = 3k, k=9. If a=-4, a^3 = -64 = 3k, k=-64/3. 9 is an option.

AI explanation

Let one root be r and the other root be r squared, so the sum of the roots is r plus r squared, which equals 12 based on the equation's coefficients. Factoring this gives r times (1 plus r) equals 12, so r equals 3. The product of the roots is r times r squared, which equals r cubed; since r equals 3, the product is 3 cubed, giving 27. From the equation, the product of the roots also equals 3k, so 3k equals 27, which means k equals 9.

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