Solving Quadratic Equations :
We now move on to difficult terrain. Once you have mastered linear equation, we now must tackle quadratic equations.
A quadratic is a polynomial that looks like ax⁰+bx+c, where a, b and c are just numbers.
In order to solve quadratic equations, you will first need to factor quadratics.
Factoring the quadratics:
For an easy case of factoring, you will need to find two numbers that will not only multiply to equal the constant term c but will all add up to equal the b the coefficient on the x term. For instance, factor the following:
X2 + 5x + 6
You need to find factors of 6 that can add up to 5. Since 6 is the product of 2 and 3 and since 2 +3 = 5, you should take 2 and 3. B y multiplying polynomials, you can get this quadratic. So by multiplying two factors of the form “(x+m)( x+n)” where m and n are numbers, you can get the above quadratic form. So draw your parenthesis with an x in front of each number and write like this: (x+2) (x+ 3). This is how you factor the above quadratic x2 + 5x + 6. Let us see how it works.
You can claim that
(x + 2) (x + 3) = X2 + 5x +6
Removing the parenthesis on the left hand side of the equation you get
X2 + 3x + 2x + 6 (you simply multiply the variable and the constant of the first parenthesis with the those of the second parenthesis)
Therefore you can write,
X2 + 5x +6 = x2 +5x +6
This is how you factor simple quadratics.
The Quadratic formula:
Sometimes you will need to use the quadratic formula to solve quadratic equations. Remember the simple quadratic polynomial ax2 + bx + c. Well, a quadratic formula is derived from the process of completing the square and is formally stated as ax2 + bx + c = 0 and the value of x is given by the formula
Let us now solve a basic quadratic equation:
Solve, x2 + 3x – 4 = 0
By factoring the quadratic you know the two factors of x are -4 and 1 (because -4 + 1 = 3 and -4 x 1 = -4)
we substitute x with its factors. Thus, using the quadratic equation we get,
x=(-3-5)/2 and x=(-3+5)/2
Therefore, x = -8/2 and 2/2
Or x = -4 and x = 1
Let's watch the video demonstration of Quadratic Equations for better understanding
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