Multiple choice

If roots of the equation $2x^2 + 3(k - 2)x + 4 - k = 15x$ are negative of each other, then $k$ equals

  1. 4

  2. 2

  3. 0

  4. 7
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D Correct answer
Explanation

Equation: 2x^2 + (3k - 6 - 15)x + (4 - k) = 0, so 2x^2 + (3k - 21)x + (4 - k) = 0. If roots are negative of each other, their sum is 0. Thus 3k - 21 = 0, so k = 7.

AI explanation

Rearranging the equation gives the standard quadratic form 2x squared plus (3k minus 21)x plus 4 minus k equals 0. For the roots to be negatives of each other, the sum of the roots must equal zero. The sum of the roots is the negative coefficient of x divided by the leading coefficient, so negative (3k minus 21) divided by 2 equals 0. Solving 3k minus 21 equals 0 gives k equals 7.

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