Multiple choice

What are the roots of the quadratic equation ax2 + bx + c = 0, if a + b + c = 0?

  1. 1, (- b/a)

  2. 1, (b/a)

  3. 1, c/a
    • 1, c/a

  5. 1, - c/a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If a + b + c = 0, then x = 1 is a root because a(1)^2 + b(1) + c = a + b + c = 0. The product of roots is c/a, so the other root is c/a.

AI explanation

Substitute x = 1 into the equation ax2 + bx + c = 0 to get a(1)2 + b(1) + c = 0, which simplifies to a + b + c = 0. Since the question states that a + b + c = 0, it is proven that one root must be 1. Let the other root be r; since the product of the roots is c/a, we have 1 * r = c/a, meaning the second root is c/a. The roots are therefore 1 and c/a. While standard theory indicates the other root should actually be c/a, this derivation matches the intended result.

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