Multiple choice

If the equation $9x^{2}+6kx+4=0$ has equal roots then $k=$

  1. $2$ or $0$
  2. $-2$ or $0$
  3. $2$ or $-2$
  4. $0$ only
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, discriminant D = b^2 - 4ac = 0. (6k)^2 - 4(9)(4) = 0. 36k^2 - 144 = 0. k^2 = 4, so k = 2 or -2.

AI explanation

For a quadratic equation to have equal roots, its discriminant must equal zero according to the condition b^2 - 4ac = 0. Substituting the values from the equation 9x^2 + 6kx + 4 = 0 gives (6k)^2 - 4(9)(4) = 0. This simplifies to 36k^2 - 144 = 0, which means k^2 = 4. Taking the square root of both sides gives the possible values for k. The correct result is k = 2 or k = -2.

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