Multiple choice

For what value of k, does the equation $[kx^{2} + (2k + 6) x + 16 = 0]$ have equal roots?

  1. $1$ and $9$
  2. $-9$ and $-1$
  3. $-1$ and $9$
  4. $-1$ and $-9$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. (2k+6)^2 - 4(k)(16) = 0. 4k^2 + 24k + 36 - 64k = 0. 4k^2 - 40k + 36 = 0. k^2 - 10k + 9 = 0. (k-1)(k-9) = 0. So k = 1 or 9.

AI explanation

For a quadratic equation to have equal roots, its discriminant must equal zero, so we set (2k + 6) squared minus 4 times k times 16 to 0. Expanding this gives 4k squared + 24k + 36 minus 64k equals 0, which simplifies to 4k squared minus 40k + 36 equals 0. Dividing by 4 yields k squared minus 10k + 9 equals 0, which factors into (k minus 1)(k minus 9) equals 0; therefore, k equals 1 and 9.

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