Algebraic equations involving variables raised to a power
By DarthVader
Date: 2021-11-17
Topic: 82 see comments
Post views: 1118
Equations with roots & exponents
Main strategy for this type of problem is:
- Factoring
Example Problem 1:
x2 - 9 = 0
Step 1:
Get the x2 to one side
x2 = 9
Step 2:
Apply a square root to both sides
√x2 = √9
Step 3:
Square root cancels the x2 exponent
x = √9
So:
x = ±3
Step 4:
You must always use a ‘plus minus’ sign as the answer could be either positive or negative
Example Problem 2:
3x2 + 9x = 0
Step 1:
Here we will have to factor out common factors of each term
3x( ) = 0
Step 2:
Now work out what must go into the parenthesis
3x(x + 3) = 0
Step 3:
Now for the equation to be true, either one of the terms must equal to zero, thus there are two solutions
Solution 1: x = 0
Solution 2: x = -3
Example Problem 3:
x2 - 5x + 6 = 0
Step 1:
Draw out two sets of parenthesis
( ) ( ) = 0
Step 2:
We will be using FOIL, so work out which two numbers will multiply to give x2 first
(x ) (x ) = 0
Step 3:
Now work out which two numbers will multiply to give 6, and add to give 5
(x 2) (x 3) = 0
Step 4:
Now work out which signs have to go between them
(x - 2) (x - 3) = 0
Step 5:
Now you must solve each equation to equal zero
(x - 2) = 0 ⇢ x = 2
(x - 3) = 0 ⇢ x = 3
Solution 1: x = 2
Solution 2: x = 3
Example Problem 3:
6x2 + 11x + 3 = 0
Step 1:
Draw out two sets of parenthesis
( ) ( ) = 0
Step 2:
We will be using FOIL, so work out which two numbers will multiply to give 6x2 first
(2x ) (3x ) = 0
Step 3:
Now work out which two numbers will multiply to give 3
(2x 3) (3x 1) = 0
Step 4:
Now work out which signs have to go between them
(2x + 3) (3x + 1) = 0
Step 5:
Now you must solve each equation to equal zero
(2x + 3) = 0
(3x + 1) = 0
Solution 1: x = -3/2
Solution 2: x = -1/3
Note: Factoring will include some trial and error so don't be afraid to input different values until you find the correct answer
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