Multiple choice

For the equation 3x2 + px + 3 = 0, p < 0, if one of the roots is square of the other, then p is equal to

  1. 6

  2. 3

  3. -6

  4. -3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Roots are alpha and alpha^2. Product of roots = c/a = 3/3 = 1. So alpha * alpha^2 = 1 => alpha^3 = 1 => alpha = 1. If alpha = 1, then the roots are 1 and 1. Sum of roots = -p/3 = 1 + 1 = 2. -p = 6, p = -6.

AI explanation

Let the roots be a and a2, then the product of the roots gives a3 = 3/3 = 1, so a = 1. The two roots are therefore 1 and 1. The sum of the roots is 1 + 1 = 2, which must equal -p/3, making p = -6.

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