QUADRATIC EQUATIONS
A quadratic equation is a quadratic expression however it contains an equal sign. There are different methods used when solving quadratic equations some of such you will be taught in this lesson.
Method 1 - Factorization method.
This method involves the same procedure as with factorizing quadratic expressions except you are going to equate your answers to zero.
Wriiten Example 1 - 4x^2 + 12x + 9 = 0
4x^2 + 12x + 9 = 0
(4x^2 + 6x)+(6x + 9) = 0
2x(2x+3) +3 (2x+3) = 0
(2x + 3) (2x +3)
2x + 3 = 0
2x/2 + 3 - 3 = 0 - 3/2
x = -3/2
Explanation -
In the above example, the same procedure as solving quadratic expressions was carried out however, they were all equated to 0. The resulting answer was "2x + 3 = 0". In this question, our answer brackets were the same so we only needed to write one. To get the "x" by itself we had to divide both sides by 2. To get rid of the "3" we had to do the opposite operation of the number which was subtraction, We subtracted 3 from both sides and gave us an answer of "x= -3/2"
Step by Step guide -
Step 1 - Identify if the given question is a quadratic expression.
Step 2 - Identify the terms in the expressions. ( a,b, and c term)
Step 3 - Write them out.
step 4 - Now find the "ac" term.
Step 5 - Identify which two numbers when multiplied equate to the "ac" term and when added or subtracted equate to the "b" term.
Step 6 - Rewrite the a term and the two numbers you found and rewrite the c term.
Step 7 - Bracket the first two terms and the last two terms of the expression written.
Step 8 - Take out what's common from the first bracket and use your result to factor out what's inside the bracket.
Step 9 - Repeat step 8 for the second bracket.
Step 10 - Ensure that the brackets are the same.
Step 10 - After results are found you are now going to place the two terms on the outside in a bracket, and rewrite one of the brackets.
Step 11 - Equate the answer to 0.
Step - If "x" isn't by itself you do the necessary operations to get it on its own.
Diagram example 2 -
Common mistakes students make:
1. When carrying numbers over the equal sign they don't change the operation sign.
2. They don't factorize correctly.
3. They don't find the correct numbers for the "ac" and the 'b" term.
Ways to fix these common mistakes :
1. Always ensure that when carrying numbers over the equal sign you change the current operation sign.
2. Always ensure that you are factorizing properly to avoid a wrong answer.
3. Ensure that the two numbers used in place of the B term are correct as explained in step 5 above.
Method 2 - Quadratic formula
The quadratic formula is a method used to solve quadratic equations if it cannot be solved using the factorization method, This mostly happens when the answer are not rational numbers.
Coefficients - A = -5, B = 6, C = 1
Step by Step guide -
Step 1 - Identify if the equation is quadratic.
Step 2 - Identify the coefficients of the given terms.
Step 3 - Plug in the given information into the quadratic formula.
Step 4 - Continue solving the questions until you arrive at your final answer.
Common mistakes made by students:
1. Doesn't follow all steps leading to a wrong answer.
2. Doesn't plug in the information properly into the formula.
3. Rush and identify coefficients.
Ways to reduce these mistakes :
1. Ensure all steps are properly carried out to get a correct answer.
2. Ensure that you plug the information into the correct areas of the formula so your answer will be correct.
3. Don't rush and check coefficients because most questions have them in different positions.
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