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

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

• A. c/a
• B. -c/a
• C. a/c
• D. b/a

Answer: (A)

The product of the roots is c/a. For a quadratic ax^2 + bx + c = 0 with a ≠ 0, you can think of it as a(x − r)(x − s) where r and s are the roots. Expanding gives ax^2 − a(r + s)x + a(rs). By matching coefficients with ax^2 + bx + c, you get the product rs = c/a and the sum r + s = −b/a. So the product is c/a. This is a direct result of how a quadratic factors and how the coefficients relate to the roots.

The product of the roots is c/a. For a quadratic ax^2 + bx + c = 0 with a ≠ 0, you can think of it as a(x − r)(x − s) where r and s are the roots. Expanding gives ax^2 − a(r + s)x + a(rs). By matching coefficients with ax^2 + bx + c, you get the product rs = c/a and the sum r + s = −b/a. So the product is c/a. This is a direct result of how a quadratic factors and how the coefficients relate to the roots.