Back to: MATHEMATICS SS1
Welcome to class!
In today’s class, we will be talking about the general form of the quadratic equation leading to the formula method. Enjoy the class!
General Form of Quadratic Equation Leading to Formula Method
The quadratic formula
Given a quadratic equation in the following form:
ax2 + bx + c = 0
…where a, b, and c are the numerical coefficients of the terms of the quadratic, the value of the variable x is given by the following equation:
X = −b± √b2 − 4ac
. 2a
The nice thing about the Quadratic Formula is that the Quadratic Formula always works. There are some quadratics (most of them, actually) that we can’t solve by factoring. But the Quadratic Formula will always spit out an answer, whether or not the quadratic expression was factorable.
Let’s try that first problem from the previous page again, but this time we’ll use the Quadratic Formula instead of the laborious process of completing the square:
Use the quadratic formula to solve x2 – 4x – 8 = 0
The quadratic formula requires that I have the quadratic expression on one side of the “equals” sign, with “zero” on the other side. They’ve given me the equation already in that form. Also, the formula is stated in terms of the numerical coefficients of the terms of the quadratic expression. Looking at the coefficients in this equation, I see that a = 1, b = –4, and c = –8. I’ll plug these numbers into the formula, and simplify. (I should get the same answer as I previously have.)
X = −(−4) ± √(−4)² − 4(1) (−8)
. 2(1)
= 4 ± √16 +32 = 4 ± √48
. 2 2
= 4 ± √16.3 = 4 ± √3
. 2 2
= 2 (2 ± 2√3) = 2 ± 2√3
. 2
This is the same answer gotten before, which confirms that the quadratic formula works as intended. Once again, my final answer is:
X = 2 ± 2√3
Solve 4x2 + 3x – 2 = 0 using the quadratic formula
First, I’ll read off the values of the coefficients that I’ll be plugging into the formula:
a = 4
b = 3
c = – 2
Now all I have to do is plug these values into the Formula, and simplify to get my answer:
X = −(3) ± √(−3)² − 4(4) (−2)
. 2(4)
= −3 ± √9 +32 = −3 ± √41
. 8 8
Nothing will simplify here, so I’m done. The answer is:
= −3 ± √41
. 8
In our next class, we will be talking about the Solution of Quadratic Equation by Graphical Method. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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