Multiple choice

For what values of k, will quadratic equation $\displaystyle { 9x }^{ 2 }+3kx+4=0$ have real and equal roots?

  1. $\displaystyle \pm 4$
  2. $\displaystyle \pm 3$
  3. $\displaystyle \pm 2$
  4. $\displaystyle \pm 1$
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A Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have real and equal roots, the discriminant D = b^2 - 4ac must be zero. Here, (3k)^2 - 4(9)(4) = 0, so 9k^2 = 144, k^2 = 16, and k = +/- 4.

AI explanation

A quadratic equation has equal roots when its discriminant is zero. Applying the discriminant formula of D = b^2 - 4ac to 9x^2 + 3kx + 4 = 0, we write (3k)^2 - 4(9)(4) = 0. This simplifies to 9k^2 = 144, which gives k^2 = 16 and means k is plus 4 or minus 4.

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