What are the important formulas in quadratic equations?

Answer 1

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Here are the important formulas in quadratic equations, in standard form ax^2 + bx + c = 0, that you need to know and remember:

1. The sum of the 2 real roots: x1 + x2 = -b/a(1)

2. The product of the 2 real roots: x1.x2 = c/a(2)

3. The Discriminant D = b^2 - 4ac (3)

4. The quadratic formula

x1 = -b/2a + squareroot of D/2a, and x2 = -b/2a- squareroot of D/2a (4)

NOTE. There is an improved quadratic formula, called the quadratic formula in graphic form, that you need to know. (Amazon e-book 2010)

The 2 real roots of a quadratic equation are given by this formula:

x1 = -b/2a + d/2a ; and x2 = -b/2a - d/2a(1)

In this formula:

The quantity (-b/2a) represent the x-coordinate of the parabola axis.

The quantities (d/2a) and (-d/2a) represent the 2 distances from the parabola axis to the two x-intercepts of the parabola.

The quantity (d) can be zero, a number (real or radical), or imaginary that will translate into a double root, 2 real roots, or no real roots.

This formula is simpler and easier to remember since we can relate it to the two x-intercepts of the parabola graph.

The quantity (d) can be compute from the relation:

d^2 = b^2 - 4ac (2)

This relation (2) can be easily obtained by writing that the product of the 2 real roots is equal to (c/a). To solve a quadratic equation, first find (d) from the relation (2), then compute the 2 real roots by the formula (1).