Note that the coefficient a is the same as in the standard form. Where r and s are the roots of the quadratic equation (they may be real, imaginary, or complex). The second form is the factored form of a quadratic equation. The constant term: c (the third term in standard form).The linear term: bx (the second term in standard form).The quadratic term: ax 2 (the first term in standard form).Where a, b, and c are real numbers and a is nonzero. The first form is the standard form of a quadratic equation (a quadratic function that is set equal to zero). Before we get into that, let’s look at two equivalent forms of a quadratic equation. We can also express the sum and product of a quadratic equation’s roots in terms of the coefficients. The signs of the coefficients of quadratic equations can tell us something about the roots. By looking at the signs of a, b, and c, we can sometimes tell when the roots will be real, imaginary, or complex. The roots and coefficients of a quadratic equation are related in numerous ways. Roots & Coefficients Of A Quadratic Equation We’ll also give proofs and examples to make the concepts clear. In this article, we’ll talk about the relationship between the roots and coefficients of a quadratic equation. For example, the sign of c can also tell us whether the y-intercept of the parabola is above or below the x-axis. Of course, the coefficients can give us other information as well. If a > 0, the parabola is convex (concave up), and a < 0 means the parabola is concave (concave down). If a & c have opposite signs, the quadratic equation will have two distinct real roots. So, what do you need to know about the roots & coefficients of a quadratic equation? For a quadratic equation ax 2 + bx + c = 0, the sum of the roots is –b/a, and the product of the roots is c/a. Knowing these formulas can make it easier to work with quadratic equations and their graphs (parabolas). The roots and coefficients of a quadratic equation can be connected by formulas that tell us about their relationship.