For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by which expression?

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by which expression?

• A. -b/a
• B. b/a
• C. -a/b
• D. a/b

Answer: (A)

For a quadratic, the sum of the roots is tied to the coefficient of x relative to the leading coefficient. If the roots are r and s, you can write the quadratic as a(x − r)(x − s). Expanding gives ax^2 − a(r + s)x + a rs. The coefficient of x is −a(r + s), and that must equal b. So −a(r + s) = b, which means r + s = −b/a. Therefore the sum of the roots is −b/a. Dividing the equation by a also shows this: the monic form x^2 + (b/a)x + c/a has the sum of roots equal to the negative of the x-coefficient, again −b/a.

For a quadratic, the sum of the roots is tied to the coefficient of x relative to the leading coefficient. If the roots are r and s, you can write the quadratic as a(x − r)(x − s). Expanding gives ax^2 − a(r + s)x + a rs. The coefficient of x is −a(r + s), and that must equal b. So −a(r + s) = b, which means r + s = −b/a. Therefore the sum of the roots is −b/a. Dividing the equation by a also shows this: the monic form x^2 + (b/a)x + c/a has the sum of roots equal to the negative of the x-coefficient, again −b/a.