How can you solve quadratic Equation in one variable using factoring method?
Answers
Quadratic equation in 1 variable is of the form
ax^2 + bx + c = 0
u can solve it using factorizationor by using quadratic formula.
Now for factorization
find 2 integers whose sum is equal to b and product equal to ac
e.g..
x^2 + 3x + 2 = 0
x^2 + x + 2x + 2 = 0
x(x + 1) + 2(x +1) = 0
(x+2)(x+1) = 0
x = -2 or -1
(x+2)(x+1) are the factors
similar e.g.
x^2 - 9x + 18
x^2 - 6x - 3x + 18
x( x -6) -3(x -6)
(x-3)(x-6)
Given : quadratic equation in one variable
To Find : How to solve factoring method
Solution:
quadratic equation in one variable can be solve d by factoring method
Generally using middle term split
ax² + bx+ c = 0
b has to be split in two parts such that sum is b and product is ac
For example
x² - 3x + 2 = 0
Here product is 2 ( + Ve)
Sum is - 3
Hence both Split should be -ve
x² - 2x - x + 2 = 0
-2 - 1 = - 3
(-2)(-1) = 2
(x - 2)(x - 1) = 0
x² + 3x + 2 = 0
Here product is 2 ( + Ve)
Sum is 3
Hence both Split should be +ve
x² +2x + x + 2 = 0
2 + 1 = - 3
(2)(1) = 2
(x + 2)(x + 1) = 0
x² - 3x - 4 = 0
Product is - 4
Sum is - 3
Hence split in two terms one negative , one positive
Negative term greater than positive term
x² - 4x + x - 4 = 0
-4 + 1 = - 3
(-4)(1) = - 4
(x - 4)(x + 1) = 0
x² + 3x - 4 = 0
Product is - 4
Sum is 3
Hence split in two terms one negative , one positive
Positive term greater than negative term
x² + 4x - x - 4 = 0
4 - 1 = - 3
(4)(-1) = - 4
(x + 4)(x - 1) = 0
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