Multiple choice

One root of the quadratic equation $x^2+px+3 =0$ is $1$. Its other root is

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

If 1 is a root of x^2 + px + 3 = 0, then 1 + p + 3 = 0, so p = -4. The equation is x^2 - 4x + 3 = 0. Factoring gives (x - 1)(x - 3) = 0. The roots are 1 and 3.

AI explanation

If x = 1 is a root of the equation x^2 + px + 3 = 0, we substitute 1 for x to get 1 + p + 3 = 0, meaning p = -4. The sum of the roots is -p/1 = 4. Since one root is 1, the other root is found by subtracting it from the sum, which gives 3.

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