Solve the equation x⁴-8x³+24x²-32x+20=0 if 3+i is a root
Answers
STEP
1
:
Equation at the end of step 1
((((x4)-(8•(x3)))+(23•3x2))-32x)+16
STEP
2
:
Equation at the end of step
2
:
((((x4) - 23x3) + (23•3x2)) - 32x) + 16
STEP
3
:
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(x) = x4-8x3+24x2-32x+16
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 16.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8 ,16
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 81.00
-2 1 -2.00 256.00
-4 1 -4.00 1296.00
-8 1 -8.00 10000.00
-16 1 -16.00 104976.00
1 1 1.00 1.00
2 1 2.00 0.00 x-2
4 1 4.00 16.00
8 1 8.00 1296.00
16 1 16.00 38416.00
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
x4-8x3+24x2-32x+16
can be divided with x-2
I hope you are understand my solution