2. Solve the following equation:
2X4-5X2+2=0
Answers
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP1:Equation at the end of step 1
((2 • (x4)) - 5x2) + 2 = 0
STEP 2 :
Equation at the end of step2:
(2x4 - 5x2) + 2 = 0
STEP3:Trying to factor by splitting the middle term
3.1 Factoring 2x4-5x2+2
The first term is, 2x4 its coefficient is 2 .
The middle term is, -5x2 its coefficient is -5 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 2 • 2 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -5 .
-4 + -1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -1
2x4 - 4x2 - 1x2 - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
2x2 • (x2-2)
Add up the last 2 terms, pulling out common factors :
1 • (x2-2)
Step-5 : Add up the four terms of step 4 :
(2x2-1) • (x2-2)
Which is the desired factorization
Trying to factor as a Difference of Squares:
3.2 Factoring: x2-2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Trying to factor as a Difference of Squares:
3.3 Factoring: 2x2-1
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step3:
(x2 - 2) • (2x2 - 1) = 0
STEP4:Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
4.2 Solve : x2-2 = 0
Add 2 to both sides of the equation :
x2 = 2
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 2
These solutions are x = ± √2 = ± 1.4142
Answer:
0, True
Step-by-step explanation:
2*4-5*2+2 = 0
8-5*2+2 = 0
8-10+2 = 0
0 = 0
Therefore the equation is True since 0 is equal to 0
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