solve by using ferrari's method x^4-4x^3+2x^2+12x=0
Answers
Step-by-step explanation:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((((x4)-(4•(x3)))-2x2)+12x)+9 = 0
STEP
2
:
Equation at the end of step
2
:
((((x4) - 22x3) - 2x2) + 12x) + 9 = 0
STEP
3
:
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(x) = x4-4x3-2x2+12x+9
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test 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 integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 9.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 0.00 x+1
-3 1 -3.00 144.00
-9 1 -9.00 9216.00
1 1 1.00 16.00
3 1 3.00 0.00 x-3
9 1 9.00 3600.00
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
x4-4x3-2x2+12x+9
can be divided by 2 different polynomials,including by x-3
Polynomial Long Division :
3.2 Polynomial Long Division
Dividing : x4-4x3-2x2+12x+9
("Dividend")
By : x-3 ("Divisor")
dividend x4 - 4x3 - 2x2 + 12x + 9
- divisor * x3 x4 - 3x3
remainder - x3 - 2x2 + 12x + 9
- divisor * -x2 - x3 + 3x2
remainder - 5x2 + 12x + 9
- divisor * -5x1 - 5x2 + 15x
remainder - 3x + 9
- divisor * -3x0 - 3x + 9
remainder 0
Quotient : x3-x2-5x-3 Remainder: 0
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x3-x2-5x-3
See theory in step 3.1
In this case, the Leading Coefficient is 1 and the Trailing Constant is -3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 0.00 x+1
-3 1 -3.00 -24.00
1 1 1.00 -8.00
3 1 3.00 0.00 x-3
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
x3-x2-5x-3
can be divided by 2 different polynomials,including by x-3