Quadratic Equation Revision Questions Form Two Basic Mathematics
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
The Solution of a Quadratic Equation by Factorization
Determine the solution of a quadratic equation by factorization
We can use any of the methods of factorization we learnt in previous chapter. But for simplest we will factorize by splitting the middle term. For Example: solve for x, x2 + 4x = 0
solution
Since the constant term is 0 we can take out x as a common factor.
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.
Quadratic Equation Revision Questions Form Two Basic Mathematics
Example 1
Solve the equation: 3x2 =- 6x – 3.
first rearrange the equation in its usual form.
that is:
3x2 = – 6x – 3
3x2 + 6x + 3 = 0
now, factorize the equation by splitting the middle term. Let us find two numbers whose product is 9
and their sum is 6. The numbers are 3 and 3. Hence the equation 3x2 + 6x + 3 = 0 can be written as:
3x2 + 3x + 3x + 3 = 0
3x(x + 1) + 3(x + 1) = 0
(3x + 3)(x + 1) (take out common factor which is (x + 1))
either (3x + 3) = 0 or (x + 1) = 0
therefore 3x = -3 or x = -1
x = -1 (divide by 3 both sides) or x = -1
Therefore, since the values of x are identical then x = -1.
