Multiple choice

If 2 is a root of the equation 2x2 + kx + 4 = 0, which of the following values of k gives another positive integer root?

  1. k = 6

  2. k = 12

  3. k = -6

  4. k = -12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 2 is a root, 2(2^2) + k(2) + 4 = 0, so 8 + 2k + 4 = 0, 2k = -12, k = -6. The equation is 2x^2 - 6x + 4 = 0. Dividing by 2: x^2 - 3x + 2 = 0. (x-1)(x-2) = 0. Roots are 1 and 2. Both are positive integers.

AI explanation

Substitute the root x = 2 into the equation 2(2)^2 + k(2) + 4 = 0 to find the value of k. This gives 8 + 2k + 4 = 0, which simplifies to 2k = -12 and k = -6. To verify, substituting k = -6 into the original equation gives 2x^2 - 6x + 4 = 0, which factors to 2(x - 2)(x - 1) = 0, yielding the other positive integer root of 1.

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