Multiple choice

If one of the roots of the equation x2 + ax + 3a = 0 is 1, then its other root is

  1. -0.25

  2. -0.75

  3. 3

  4. Will depend on the value of a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If 1 is a root, 1^2 + a(1) + 3a = 0, so 1 + 4a = 0, a = -0.25. The equation is x^2 - 0.25x - 0.75 = 0. The product of roots is c/a = -0.75. Since one root is 1, the other is -0.75.

AI explanation

Since x = 1 is a root of the equation x2 + ax + 3a = 0, substitute 1 for x to get 12 + a(1) + 3a = 0. This simplifies to 1 + 4a = 0, so a = -1/4. The product of the roots for a quadratic equation is given by c/a, so 1 times the other root equals 3a. Substituting a = -1/4 gives the other root as 3(-1/4), which is -0.75.

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