Multiple choice

If the equation x2 - (k + 4)x + (4k + 1) = 0 has equal roots,

  1. k = 6

  2. k = 2

  3. k = 6, 2

  4. k = ±6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, the discriminant b^2 - 4ac must be zero. Here, (-(k+4))^2 - 4(1)(4k+1) = 0. Expanding gives k^2 + 8k + 16 - 16k - 4 = 0, which simplifies to k^2 - 8k + 12 = 0. Factoring gives (k-6)(k-2) = 0, so k = 6 or k = 2.

AI explanation

For a quadratic equation to have equal roots, its discriminant (b^2 - 4ac) must equal zero. Substituting the coefficients gives (-(k+4))^2 - 4(1)(4k+1) = 0, which expands to k^2 - 8k + 12 = 0. Factoring this quadratic yields (k - 6)(k - 2) = 0, proving the values of k are 6 and 2.

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