Multiple choice

The equation $9x^2+3kx+4=0$ has repeated roots, when $k$ is equal to

  1. $\pm 1$
  2. $\pm 2$
  3. $\pm 3$
  4. $\pm 4$
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D Correct answer
Explanation

For repeated roots, the discriminant b^2 - 4ac must be 0. (3k)^2 - 4(9)(4) = 0 => 9k^2 = 144 => k^2 = 16 => k = +/- 4.

AI explanation

For a quadratic equation to have repeated roots, its discriminant, calculated as b squared minus 4 times a times c, must equal zero. Substituting the coefficients a = 9, b = 3k and c = 4 into this formula gives (3k) squared minus 4 multiplied by 9 multiplied by 4, which simplifies to 9k squared minus 144 equals 0. Solving for k, we get 9k squared equals 144, leading to k squared equals 16. Taking the square root gives the final result that k equals plus or minus 4.

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