TOPIC 3: QUADRATIC EQUATIONS ~ MATHEMATICS FORM 2
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.
Solving Equations
The standard form of a Quadratic equation is ax2 + bx + c =0whereby a, b, c are known values and ‘a’ can’t be 0. ‘x’ is a variable (we don’t know it yet). a is the coefficient of x2 , b is the coefficient of x and c is a constant term. Quadratic equation is also called an equation of degree 2 (because of the 2 on x). There are several methods which are used to find the value of x. These methods are:
- by Factorization
- by completing the square
- by using quadratic formula
So, x2 + 4x = x(x + 4) = 0. This means the product of x and (x + 4) is 0. Then, either x = 0 or x + 4 = 0. If x + 4 = 0 that is x = -4. Therefore the solution is x = 0 or x = -4.
Example 1
Example 2
Example 3
Therefore
Example 4
The Solution of a Quadratic Equation by Completing the Square
Find the solution of a quadratic equation by completing the square
Completing the square.
General Solution of Quadratic Equations
The special quadratic formula used for solving quadratic equation is:
Quadratic Equations using Quadratic Formula
Solve quadratic equations using quadratic formula
Example 8
solve 5x2 – 8x + 3 = 0 by using quadratic formula.
Example 9
Word problems leading to quadratic equations
Given a word problem; the following steps are to be used to recognize the type of equation.
Example 10
since we don’t have negative dimensions, then the width is 12cm and the length is 12 + 8 = 20cm
Example 11
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