Multiple choice

The value of k, of the roots of the equation $ \displaystyle 2kx^{2}+2kx+2=0 $ are equal is

  1. $ \displaystyle \frac{4}{5} $
  2. $4$
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a quadratic equation to have equal roots, its discriminant must be zero. Setting the discriminant of 2kx^2 + 2kx + 2 = 0 to zero gives (2k)^2 - 4(2k)(2) = 0, which simplifies to 4k(k - 4) = 0. Since k cannot be zero for the equation to remain quadratic, we find k = 4.

AI explanation

For a quadratic equation to have equal roots, its discriminant b squared minus 4 times a times c must equal zero. Substituting the coefficients from the given equation into the discriminant formula gives (2k) squared minus 4 multiplied by 2k multiplied by 2, which simplifies to 4k squared minus 16k equals 0. Factoring out 4k gives 4k multiplied by the quantity (k minus 4) equals 0, yielding k = 0 or k = 4; because a quadratic equation requires the highest degree coefficient to be non-zero, the valid solution is k = 4.

Keep practicing — related questions