### #ezw_tco-2 .ez-toc-widget-container ul.ez-toc-list li.active{ background-color: #ededed; } chapter outline

‘Quad’ means square, and the variable is squared (order 2). Thus, a quadratic equation is an algebraic equation of the second degree written in the form:

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ax2 + bx + c, here ‘a’ and ‘b’ are the coefficients, ‘x’ is the variable, ‘c’ is a constant

ax2 + bx + c, here ‘a’ and ‘b’ are the coefficients, ‘x’ is the variable, ‘c’ is a constant

This is the standard form of the quadratic equation. For an equation to be quadratic, the coefficient of x2 will be a non-zero term (a ≠ 0)

Some examples of quadratic equations are:

x2 + 2x – 15 = 0, here a = 1, b = 2, and c =-15

x2 – 49x = 0, here a = 1, b = -49, and c = 0

Sometimes the quadratic equations are outside the standard form and are disguised. In such cases, they were arranged and brought into the standard form. Some examples of such instances are shown below:

2x2 -36 = x

Rearranging this equation, we get

2x2 – x – 36 = 0, this equation is now in the standard form

Similarly, for the equation

(a – 4)2 – 9 = 0

=> a2 – 8a + 16 – 9 = 0

=> a2 – 8a + 7 = 0

## How to Solve Quadratic Equations

The solutions to the quadratic equations are its two roots, also called zeros. The simplest way to find the two roots is by using the quadratic formula:

x = ${x=\dfrac{-b\pm \sqrt{b^{2}-4ac}}{2a}}$
• ${x=\dfrac{-b+\sqrt{b^{2}-4ac}}{2a} }$