Multiple choice

If the roots of the quadratic equation $5x^{2} - 2kx + 20 = 0$ are real and equal then the value of $k$ is ________.

  1. $20$
  2. $-10$
  3. $10$ or $-10$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For real and equal roots, the discriminant D = b^2 - 4ac = 0. (-2k)^2 - 4(5)(20) = 0. 4k^2 - 400 = 0. k^2 = 100, so k = 10 or -10.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to have real and equal roots, its discriminant (b^2 - 4ac) must be zero. Substituting the values a = 5, b = -2k, and c = 20 into the discriminant formula gives (-2k)^2 - 4(5)(20) = 0. Simplifying this yields 4k^2 - 400 = 0, so 4k^2 = 400 and k^2 = 100. Taking the square root gives the result k = 10 or k = -10.

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