Solving quadratic equations can be difficult, but luckily there are several different methods that we can use depending on what type of quadratic that we are trying to solve. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.
The Quadratic Formula
Derive the quadratic formula
The special quadratic formula used for solving quadratic equation is:
Quadratic Equations using Quadratic Formula
Solve quadratic equations using quadratic formula
solve 5x2 – 8x + 3 = 0 by using quadratic formula.
solve this quadratic equation by using quadratic formula: 3x2 = – 7x – 4
Word problems leading to quadratic equations
Given a word problem; the following steps are to be used to recognize the type of equation.
Step1: choose the variables to represent the information
Step 2: formulate the equation according to the information given
Step 3: solve the equation by using any of the method you know
In order to be sure with your answers, check if the solution you obtained is correct.
the length of a rectangular plot is 8 centimeters more than the width. If the area of a plot is 240cm2, find the dimensions of length and width.
The length of a plot is 8 more than the width, so the length of a plot be x + 8
We are given the area of a plot = 240cm2 and the area of a rectangle is given by length ×width
then solve the equation to find the value of x
Solving by splitting the middle term, two numbers whose product is -240 and their sum is 8, the number
our equation becomes; x2 + 20x – 12x – 240 = 0
x(x + 20) – 12(x + 20) = 0
either (x – 12) = 0 or (x + 20) = 0
since we don’t have negative dimensions, then the width is 12cm and the length is 12 + 8 = 20cm
Therefore the rectangular plot has the length of 20cm and the width of 12cm.
A piece of wire 40cm long is cut into two parts and each part is then bent into a square. If the sum of the areas of these squares is 68 square centimeters, find the lengths of the two pieces of wire.
1. Solve each of the following quadratic equations by using factorization method:
- -6x2+ 23x – 20 = 0
- X2– x -12 = 0
2. Solve these equations by completing the square: