Multiple choice

Determine the values of $p$ for which the quadratic equation $2x^2 + px + 8 = 0$ has equal roots.

  1. $p=\pm 64$
  2. $p=\pm 8$
  3. $p=\pm 4$
  4. $p=\pm 16$
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B Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, p^2 - 4(2)(8) = 0. p^2 - 64 = 0, so p^2 = 64, p = +/- 8.

AI explanation

A quadratic equation has equal roots when its discriminant (b^2 - 4ac) is zero. Substituting a = 2, b = p, and c = 8 gives p^2 - 4(2)(8) = 0. This simplifies to p^2 - 64 = 0, meaning p^2 = 64. Taking the square root of both sides results in p = plus or minus 8.

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