Multiple choice

If the roots of the equation 4x2 – 4px + 7p – 12 = 0 are equal, find the value of p.

  1. 3 or 5

  2. 2 or 5

  3. 3 or 4

  4. 2 or 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, (-4p)^2 - 4(4)(7p - 12) = 0. This simplifies to 16p^2 - 16(7p - 12) = 0, or p^2 - 7p + 12 = 0. Factoring gives (p - 3)(p - 4) = 0, so p = 3 or p = 4.

AI explanation

For the roots of the quadratic equation to be equal, the discriminant must be zero, so we set b^2 - 4ac = 0. Substituting a = 4, b = -4p, and c = 7p - 12 gives (-4p)^2 - 4(4)(7p - 12) = 0. Expanding this yields 16p^2 - 112p + 192 = 0, and dividing by 16 simplifies it to p^2 - 7p + 12 = 0. Factoring the quadratic gives (p - 3)(p - 4) = 0, so the value of p is 3 or 4.

Keep practicing — related questions