Multiple choice

If the equation $4x^{2} + x(p + 1) + 1 = 0$ has exactly two equal roots, then one of the values of $p$ is

  1. $5$
  2. $-3$
  3. $0$
  4. $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac must be zero. Here, (p+1)^2 - 4(4)(1) = 0, so (p+1)^2 = 16. This means p+1 = 4 or p+1 = -4, so p = 3 or p = -5.

AI explanation

For the equation 4x^2 + x(p + 1) + 1 = 0 to have exactly two equal roots, its discriminant (b^2 - 4ac) must equal zero. Substituting a = 4, b = (p + 1), and c = 1 into the discriminant formula gives (p + 1)^2 - 4(4)(1) = 0. Expanding the binomial yields p^2 + 2p + 1 - 16 = 0, which simplifies to p^2 + 2p - 15 = 0. Factoring this quadratic equation gives (p + 5)(p - 3) = 0, so the values of p are -5 and 3; therefore, one of the values is 3.

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