Multiple choice

If the quadratic equation kx (x – 2) + 6 = 0 has equal roots, then the value of 'k' is

  1. 5

  2. 4

  3. 3

  4. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The equation is kx^2 - 2kx + 6 = 0. For equal roots, the discriminant D = b^2 - 4ac must be 0. Here, (-2k)^2 - 4(k)(6) = 0, which simplifies to 4k^2 - 24k = 0. Factoring gives 4k(k - 6) = 0. Since k cannot be 0 for a quadratic, k = 6.

AI explanation

Rewrite the given quadratic equation in standard form by expanding kx(x - 2) + 6 = 0 to get kx2 - 2kx + 6 = 0. For a quadratic equation to have equal roots, its discriminant (b2 - 4ac) must equal zero. Substituting the coefficients gives (-2k)2 - 4(k)(6) = 0, which simplifies to 4k2 - 24k = 0. Factoring out 4k results in 4k(k - 6) = 0, and since k cannot be zero for a quadratic equation, the value of k is 6.

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