GRE Algebra | Solving Quadratic Equations

In algebra, a quadratic equation can be written in the form:

ax^{2}+ bx + c = 0

where x is the variable and a, b, c are the real numbers and a≠0. If a=0 then it will be a linear equation not quadratic because no second order term.

If quadratic equation has solution then it can be found by using the **quadratic formula**.

**Example-1:**Solve the quadratic equation for x,x

^{2}+ 10x -24 = 0**Solution:**In the quadratic equation, we have,a=1, b=10 and c=-24

Therefore the quadratic formula yields

Hence, two solutions for the above equations are:

x = 4/2 = 2, And x = -24/2 = -12

**Example-2:**Solve the quadratic equation using factorization,x

^{2}+ 2x - 15 = 0**Solution:**Given equation,x

^{2}+ 2x - 15 = 0It can be factorize as,

x

^{2}-3x + 5x - 15 = 0 x(x - 3) + 5(x - 3) = 0 (x - 3)(x + 5) = 0Hence, two solutions for x are:

x = 3 and x = -5