Find roots of polynomial $p (x) = r^{8} - 4 r^{6} + 4 r^{4} + 4 r^{3}$

Answer

The roots of polynomial $p (r)$ are:
$r_{1} r_{2} r_{3} r_{4} r_{5} r_{6} = 0 = - 1.8617 = - 0.6421 + 0.616 i = - 0.6421 - 0.616 i = 1.5729 + 0.4897 i = 1.5729 - 0.4897 i$

Explanation

Step 1:

Factor out $r^{3}$ from $r^{8} - 4 r^{6} + 4 r^{4} + 4 r^{3}$ and solve two separate equations:

r^{8} - 4 r^{6} + 4 r^{4} + 4 r^{3} r^{3} \cdot (r^{5} - 4 r^{3} + 4 r + 4) r^{3} = 0 or r^{5} - 4 r^{3} + 4 r + 4 = 0 = 0 = 0

One solution is $r = 0$ . Use second equation to find the remaining roots.

Step 2:

Polynomial $r^{5} - 4 r^{3} + 4 r + 4$ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

Download Png

This page was created using

Polynomial Roots Calculator

About the Author

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas.

If you want to contact me, probably have some questions, write me using the contact form or email me on mathhelp@mathportal.org.

Send Me A Comment

Main Navigation

Online Math Calculators

Find roots of polynomial p(x)=r8−4r6+4r4+4r3

The roots of polynomial p(r) are: r1​r2​r3​r4​r5​r6​​=0=−1.8617=−0.6421+0.616i=−0.6421−0.616i=1.5729+0.4897i=1.5729−0.4897i​

Find roots of polynomial $p (x) = r^{8} - 4 r^{6} + 4 r^{4} + 4 r^{3}$

The roots of polynomial $p (r)$ are:
$r_{1} r_{2} r_{3} r_{4} r_{5} r_{6} = 0 = - 1.8617 = - 0.6421 + 0.616 i = - 0.6421 - 0.616 i = 1.5729 + 0.4897 i = 1.5729 - 0.4897 i$