Multiple choice

If one root of the quadratic equation $ax^{2}+bx+c=0$ is $3- 4i$, then $31a+b+c$ is equal to

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

If 3-4i is a root, 3+4i is also a root. The quadratic is (x - (3-4i))(x - (3+4i)) = x^2 - 6x + 25 = 0. Comparing with ax^2 + bx + c = 0, a=1, b=-6, c=25. 31a+b+c = 31(1) - 6 + 25 = 50. 2c = 2(25) = 50.

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