## Step by step solution :

## Step 1 :

Equation at the over of step 1 : ((x4) - 3x2) - 4 = 0## Step 2 :

Trying to lớn factor by splitting the middle term2.1Factoring x4-3x2-4 The first term is, x4 its coefficient is 1.The middle term is, -3x2 its coefficient is -3.The last term, "the constant", is -4Step-1 : Multiply the coefficient of the first term by the constant 1•-4=-4Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3.Bạn đang xem: Precalculus

-4 | + | 1 | = | -3 | That"s it |

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step2above, -4 and 1x4 - 4x2+1x2 - 4Step-4 : showroom up the first 2 terms, pulling out lượt thích factors:x2•(x2-4) địa chỉ up the last 2 terms, pulling out common factors:1•(x2-4) Step-5:Add up the four terms of step4:(x2+1)•(x2-4)Which is the desired factorization

### Polynomial Roots Calculator :

2.2 Find roots (zeroes) of : F(x) = x2+1Polynomial Roots Calculator is a phối of methods aimed at finding values ofxfor which F(x)=0 Rational Roots demo 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 and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 và the Trailing Constant is 1. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 Let us chạy thử ....

PQP/QF(P/Q)Divisor-1 | 1 | -1.00 | 2.00 | ||||||

1 | 1 | 1.00 | 2.00 |

Polynomial Roots Calculator found no rational roots

Trying lớn factor as a Difference of Squares:2.3 Factoring: x2-4 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 = bố is the commutative property of multiplication. Lưu ý : -AB+ AB equals zero and is therefore eliminated from the expression.Check: 4 is the square of 2Check: x2 is the square of x1Factorization is :(x + 2)•(x - 2)

Equation at the kết thúc of step 2 :(x2 + 1) • (x + 2) • (x - 2) = 0

## Step 3 :

Theory - Roots of a sản phẩm :3.1 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 separatelyIn other words, we are going to lớn solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.Solving a Single Variable Equation:3.2Solve:x2+1 = 0Subtract 1 from both sides of the equation:x2 = -1 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 In Math,iis called the imaginary unit. It satisfies i2=-1. Both i & -i are the square roots of -1The equation has no real solutions. It has 2 imaginary, or complex solutions.x= 0.0000 + 1.0000 i x= 0.0000 - 1.0000 i

Solving a Single Variable Equation:3.3Solve:x+2 = 0Subtract 2 from both sides of the equation:x = -2

Solving a Single Variable Equation:3.4Solve:x-2 = 0Add 2 khổng lồ both sides of the equation:x = 2

### Supplement : Solving Quadratic Equation Directly

Solving x4-3x2-4 = 0 directly Earlier we factored this polynomial by splitting the middle term.Xem thêm: Tác Dụng Của Tinh Dầu Hoa Anh Thảo, 10 Lợi Ích Của Dầu Hoa Anh Thảo Và Cách Sử Dụng

Let us now solve the equation by Completing The Square và by using the Quadratic Formula

Solving a Single Variable Equation:

Equations which are reducible khổng lồ quadratic :4.1Solvex4-3x2-4 = 0This equation is reducible to lớn quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using w, such that w = x2 transforms the equation into:w2-3w-4 = 0Solving this new equation using the quadratic formula we get two real solutions: 4.0000or-1.0000Now that we know the value(s) of w, we can calculate x since x is √ w Doing just this we discover that the solutions of x4-3x2-4 = 0are either:x =√ 4.000 = 2.00000 or:x =√ 4.000 = -2.00000 or:x =√-1.000 = 0.0 + 1.00000 i or:x =√-1.000 = 0.0 - 1.00000 i