4x^4-1=0

This solution đơn hàng with factoring binomials using the difference of squares.

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Step by Step Solution

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Step by step solution :

Step 1 :

Equation at the over of step 1 : 22x4 - 1 = 0

Step 2 :

Trying lớn factor as a Difference of Squares:2.1 Factoring: 4x4-1 Theory : A difference of two perfect squares, A2-B2can be factored into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ AB - B2 = A2 - B2Note : AB = cha is the commutative property of multiplication. Lưu ý : -AB+ AB equals zero & is therefore eliminated from the expression.Check: 4 is the square of 2Check: 1 is the square of 1Check: x4 is the square of x2Factorization is :(2x2 + 1)•(2x2 - 1)

Polynomial Roots Calculator :

2.2 Find roots (zeroes) of : F(x) = 2x2 + 1Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor which F(x)=0 Rational Roots kiểm tra is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then p is a factor of the Trailing Constant & Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 2 và the Trailing Constant is 1. The factor(s) are: of the Leading Coefficient : 1,2 of the Trailing Constant : 1 Let us test ....

PQP/QF(P/Q)Divisor
-11 -1.00 3.00
-12 -0.50 1.50
11 1.00 3.00
12 0.50 1.50

Polynomial Roots Calculator found no rational roots

Trying to lớn factor as a Difference of Squares:2.3 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 kết thúc of step 2 :

(2x2 + 1) • (2x2 - 1) = 0

Step 3 :

Theory - Roots of a sản phẩm :3.1 A sản phẩm of several terms equals zero.When a hàng hóa of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going lớn solve as many equations as there are terms in the productAny solution of term = 0 solves hàng hóa = 0 as well.

Solving a Single Variable Equation:3.2Solve:2x2+1 = 0Subtract 1 from both sides of the equation:2x2 = -1 Divide both sides of the equation by 2:x2 = -1/2 = -0.500 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ -1/2 In Math,iis called the imaginary unit. It satisfies i2=-1. Both i và -i are the square roots of -1Accordingly, √ -1/2 =√ -1•1/2= √-1•√ 50% =i•√ một nửa The equation has no real solutions.

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It has 2 imaginary, or complex solutions.x= 0.0000 + 0.7071 i x= 0.0000 - 0.7071 i

Solving a Single Variable Equation:3.3Solve:2x2-1 = 0Add 1 to lớn both sides of the equation:2x2 = 1 Divide both sides of the equation by 2:x2 = 1/2 = 0.500 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 50% The equation has two real solutions These solutions are x = ±√ 0.500 = ± 0.70711

Four solutions were found :

x = ±√ 0.500 = ± 0.70711x= 0.0000 - 0.7071 ix= 0.0000 + 0.7071 i