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Help please! and show all steps​

Help please! and show all steps​-example-1
User Bill Gale
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1 Answer

1 vote

Answer:

(x+3)(x+2)=0

x = -3

x = -2

x = 0.0000 + 1.0000 i

Explanation:

x^4 - 5x^3 +7x^2-5x+6 =0

We need to find the factors for 6 when multiplied together they give us 6

And when they are added they add up to 5

(x+3)(x+2)=0

x = -3

x = -2

x = 0.0000 + 1.0000 i

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

of -x5/ x3-2x2+x-2 and of -x5 / x^2- 2x2 and x^4-2x2 2x2

Which also separates 7 the same x7- 2x2+x-2 +x-2 and again to make (6 of the 7 )is 2x2 + x then +x to make 7

The first one can be divided with x-2 +1

Proof

3.5 Find roots (zeroes) of : F(x) = x2+1

3.4 Polynomial Long Division

Dividing : x3-2x2+x-2

("Dividend")

By : x-2 ("Divisor")

dividend x3 - 2x2 + x - 2

- divisor * x2 x3 - 2x2

remainder x - 2

- divisor * 0x1

remainder x - 2

- divisor * x0 x - 2

remainder 0

Quotient : x2+1 Remainder: 0

See theory in step 3.1

In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1

Let us test

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 24.00

-2 1 -2.00 100.00

-3 1 -3.00 300.00

-6 1 -6.00 2664.00

1 1 1.00 4.00

2 1 2.00 0.00 x-2

3 1 3.00 0.00 x-3

6 1 6.00 444.00

User Alexandr Viniychuk
by
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