Solving Quadratic Equations

Quadratic equations are solved using four main methods at GCSE: factorising worksheets, completing the square worksheets, quadratic formula worksheets and simultaneous equations worksheets. When Quadratic Equations are mapped on to graphs they form "U" shaped curves called parabolas. The image below shows x² + 10x - 13.  This quadratic equation can be solved using the quadratic formula.

The Quadratic Formula

The quadratic formula is given below. The quadratic formula when ax² + bx + c is [- b ± √(b² - 4ac)]/ 2a. a is the first coefficient before x², b is the second coefficient before x and c is a contact where x has highest power of zero. b and c might take a value of zero.

What Are Quadratic Equations?

Quadratic Equations take the form ax² + bx + c. The highest power of x is 2, or x². Quadratic Equations is a GCSE Higher topic. We usually learn how to solve quadratic equations after we know how to simplify expressions, and solve linear equations. Once students know how to solve quadratic equations students learn about Quadratic Graphs. When we solve quadratic equations we usually obtain two solutions. However, a quadratic equation can have only one (real) solution or no (real) solutions.

Solve x² + 9x + 18 = 0

Using the quadratic formula to solve x² + 9x + 18 = 0. a takes a value of 1, b takes the value + 9 and c takes the value + 18. In the case of x² - 9x - 18 = 0, b and c would be - 9 and - 18 respectively. The final answer is given below.

Quadratic Equation 2

The quadratic equation below is 3x² + 12x - 3. When 3x² + 12x - 3 = 0, solve it using the quadratic formula.