Multiple choice

If the roots of the equation $X^{2} - 8X + C = 0$, are equal then $C$ is equal to _______.

  1. $(16)$
  2. $(6)$
  3. $5$
  4. $(4)$
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A Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, (-8)^2 - 4(1)(C) = 0, so 64 - 4C = 0, which means C = 16.

AI explanation

For a quadratic equation to have equal roots, its discriminant must be zero. The discriminant is calculated as the square of the coefficient of x minus four times the product of the coefficient of x squared and the constant term. Using the given equation, we calculate the discriminant as 8 squared minus 4 times 1 times C, which gives 64 minus 4C. Setting this to zero yields 4C equals 64, so C equals 16.

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