Multiple choice

If one of the zeros of the quadratic polynomial $2x^2 + px + 4$ is 2, find the other zero. Also find the value of p

  1. $p=-1$, other zero $=1$
  2. $p=-2$, other zero $=1$
  3. $p=-6$, other zero $=1$
  4. $p=-7$, other zero $=1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 2 is a root of 2x^2 + px + 4 = 0, then 2(4) + 2p + 4 = 0, so 2p = -12, p = -6. The polynomial is 2x^2 - 6x + 4. Dividing by 2: x^2 - 3x + 2 = 0. Roots are (x-2)(x-1)=0. The other root is 1.

AI explanation

Because one zero of 2x^2 + px + 4 is 2, substituting x = 2 gives 2(2)^2 + p(2) + 4 = 0, so 8 + 2p + 4 = 0 and p equals -6. The product of the zeros equals 4/2 = 2, so multiplying the known root 2 by the other root gives 2 times the other root = 2, meaning the other root is 1.

Keep practicing — related questions