Multiple choice

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

  1. $\displaystyle \pm \sqrt { 3 } $
  2. $\displaystyle \pm \sqrt { 6 } $
  3. $\displaystyle \pm 6$
  4. $\displaystyle \pm 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, discriminant D = b^2 - 4ac = 0. k^2 - 4*3*3 = 0 => k^2 = 36 => k = +/- 6.

AI explanation

The condition for a quadratic equation to have real and equal roots is that its discriminant equals zero. Using the discriminant formula of D = b^2 - 4ac for 3x^2 + kx + 3 = 0, we establish that (k)^2 - 4(3)(3) = 0. This simplifies to k^2 = 36, meaning the values of k are plus 6 and minus 6.

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