Quadratic Equations Definition
The quadratic equation is the equation whose rank is the highest of the variables is two.
Quadratic Equations General Forms
ax2 + bx + c = 0
Information:
a ≠ 0 with a, b, c, ∈ rill number
Finding the solution of a quadratic equation means finding the value of x such that if the substituted value would satisfy that requirement. Solving the quadratic equation is also called the root of the quadratic equation.
How to Solve Quadratic Equations
Some ways that can be used to solve the quadratic equation include:- Factorization
- Complete perfect squares
- Quadratic formula
1. Solving Quadratic Equations by Factoring
Using the multiplication property of a rill number, that is, if two rill numbers are multiplied the result is zero. Thus, one of these numbers is zero or both equals zero.if p x q = 0 then p = 0 or q = 0
Quadratic Equations Example
Look for the roots of x2 + 2x - 8 = 0 !Quadratic Equations Solution by Factoring
To solve the equation x2 + 2x - 8 = 0, first find two numbers that meet the following conditions:The multiplication result is equal to a x c
The sum result is equal to b
For example, two qualifying numbers are α and β, then:
αβ = ac
α + β = b
Thus, the form factor is:
(ax + α)(ax + β) = 0
By dividing a on the left and right sides, it will get the original form.
From the equation x2 + 2x - 8 = 0 is obtained:
a = 1
b = 2
c = -8
Find the two numbers that make the multiply result = 1 x (-8) = -8, and the sum result = 2. The eligible numbers are 4 and -2. So:
So the roots of x2 + 2x - 8 = 0 are -4 and 2
2. Solving Quadratic Equations by Completing The Perfect Square
The quadratic equation ax2 + bx + c = 0, is converted to equation in the following way:Make sure the coefficient of x2 is 1, if not divide by a number such that the coefficient becomes 1.
Add left and right sides with half coefficient of x then squared.
Make the left side into a quadratic form, while the right-hand side is manipulated, making it a simpler form.
Quadratic Equation Example
By completing the perfect squares find the roots of x2 - 4x - 5 = 0!Quadratic Equation Solution by Completing The Perfect Square
x2 - 4x - 5 = 0x2 - 4x = 5
The coefficient of x2 is 1
Add left and right sides with half coefficient of x then squared.
Make the left side into a quadratic form, while the right-hand side is manipulated, making it a simpler form.
So the roots of x2 - 4x - 5 = 0 are 5 or -1
3. Solving Quadratic Equations Using Quadratic Formula
Here is the quadratic formula:Quadratic Equation Example
Find the settlement of x2 - 6x + 9 = 0 using the formula of squares!Quadratic Equation Solution Using Quadratic Formula
From x2 - 6x + 9 = 0 obtained:a = 1
b = -6
c = 9
Then:
Then the roots of x2 - 6x + 9 = 0 are 3.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
Jika ingin bertanya secara privat, Silahkan hubungi no 085709994443 dan untuk berkomentar silahkan klick link di bawah ini 👇