Quadratic Equation Tutorial

Quadratic Equation Definition:

A quadratic equation is a polynomial equation of the second degree. The general form is ax²+bx+c=0, where a ≠0.

Example 1 :

Calculate the roots(x1, x2) of the quadratic equation, x² + 2x - 8 = 0.

Step 1:

From the above equation, the value of a = 1, b = 2 and c = - 8.

Step 2:

To Find X: Substitute the values in the formula below x = (- b ±√ b² - 4 * a * c) / 2 * a

Step 3:

We get the roots, x = (- 2 ±√ 2² - 4 * 1 * - 8) / 2 * 1 x = - 4 and x = 2 which means x1 = - 4 and x2 = 2.

Example 2 :

Calculate the roots(x1, x2) of the quadratic equation, x² - 10x + 25 = 0

Step 1:

From the above equation, the value of a = 1, b = - 10 and c = 25.

Step 2:

To Find X: Substitute the values in the formula below x = (- b ±√ b² - 4 * a * c) / 2 * a

Step 3:

We get the roots, x = (- 2 ±√ 2² - 4 * 1 * - 8) / 2 * 1 x = 5 and x = 5 which means x1 = 5 and x2 = 5. Here x = 5 is called the double root. A quadratic will have a double root if the quadratic is a perfect square trinomial.