Multiple choice

Find k for which the quadratic equations $4x^{2}+3kx+1=0$ has equal root.

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

For equal roots, the discriminant D = b^2 - 4ac = 0. (3k)^2 - 4(4)(1) = 0. 9k^2 = 16. k^2 = 16/9. k = +/- 4/3.

AI explanation

For a quadratic equation to have equal roots, its discriminant must equal zero, so using the formula b squared minus 4ac equals 0. Substituting the coefficients gives (3k) squared minus 4(4)(1) equals 0, which simplifies to 9k squared minus 16 equals 0. Solving for k yields k squared equals 16 over 9, so k equals plus or minus 4 over 3.

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