Multiple choice

If one root of the equation $\displaystyle x^{2}+px+12=0 $ is $4$ while the equation $\displaystyle x^{2}+px+q=0$ has equal roots, then one value of $q$ is

  1. $3$
  2. $12$
  3. $\displaystyle \frac{49}{4}$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since 4 is a root of x^2 + px + 12 = 0, we have 16 + 4p + 12 = 0, so 4p = -28, p = -7. The second equation x^2 - 7x + q = 0 has equal roots, so the discriminant D = b^2 - 4ac = 49 - 4q = 0, giving q = 49/4.

AI explanation

Substitute the root x = 4 into the first equation x^2 + px + 12 = 0 to get 16 + 4p + 12 = 0, which yields p = -7. The second equation becomes x^2 - 7x + q = 0, and for it to have equal roots, its discriminant must be zero. Therefore, (-7)^2 - 4(1)(q) = 0, or 49 - 4q = 0. Solving this gives q = 49/4.

Keep practicing — related questions