Tips to Solve a Quadratic Equation
A quadratic equation is what makes up a quadratic formula. An example of a general quadratic equation would be: ax? + bx + c = 0 (“a” cannot be zero). Of course, if you want to solve this equation, you need to find the “x” values so that the equation will become true. Here, “x” would be the “roots” of the quadratic. These quadratic equations can have 0 to 2 “roots”.
From a quadratic equation, you can form a quadratic form so that you can complete the square. It always follows that a general quadratic equation has “roots”. For the example above, this would be:
As you can see, the quadratic formula with the quadratic equation consists of two formulas. When you read “?”, it should be read as “plus or minus”. This means, you need to work out the formula 2x. For the first time, with the “plus” sign and for the second time, with the “minus” sign. Here are the succeeding steps:
Step 1- Identify the coefficients. These would be the “a”, “b” & “c” in the sample quadratic equation above. This is important so that you can substitute the coefficients into the quadratic formula and calculate “x”. This would look like:
x? – 4x – 5 = 0
take note that there’s no number in front of “x?”. You can just think of it as “1x?”. This would then become:
a = 1, b = -4, and c = -5
If you will substitute the values into the quadratic formula, you will get:
To simplify the square root term, this would appear like:
To calculate the square root, this would show:
or
Tips to Manually Solving a Quadratic Equation
There are different ways to solve a quadratic equation through a quadratic formula. Given the example:
ax? + bx + c = 0
The quadratic formula would be:
x = [-b ? ?(b? – 4ac)]/2a
To solve this you can:
1. Initially determine if you need to make use of the quadratic formula. Take note that you only need to use it of the quadratic equation cannot be “put into brackets” or factorized. If you are asked to round off the answers or just leave it in ‘surd” (root) form, this would mean that the quadratic equation can no longer be factorized.
2. Prior to substituting numbers into the quadratic formula, just write down the values of “a”, “b” & “c”. Be careful with the positive and negative signs.
3. You can also put a bracket around the numbers every time you substitute the values into the calculator. Also check if you have an up-to-date calculator. You should be able to enter calculations as they appear on the page. Just hit the fraction key at the beginning of the calculation.
There are easy ways to use the quadratic formula for solving a quadratic equation. Follow the tips to help you use the quadratic formula.
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