Analyzing and Solving Polynomial Equations

1 V T2u061f29 5 KSuHtRa9 qSTo4fPtgwIaBrheo s JAIlElG Krri4gBh9t9sq t 5 MlavdGey ZwsiatJhc CI8nbf2iPnYimtsez VAhl4gJe6bqrcak by Kuta Software LLCKuta Software - Infinite Algebra 2 Name_____ Period____Date_____Analyzing and Solving Polynomial EquationsState the number of complex roots, the possible number of real and imaginary roots, the possiblenumber of positive and negative roots, and the possible rational roots for each equation. Then find ) x4 5 x2 36 = 02) x3 + 3 x2 14 x 20 = 03) x3 2 x2 + 3 x 6 = 04) x4 14 x2 + 45 = 05) x4 + 6 x2 + 8 = 06) x4 + 3 x2 18 = 07) x3 1 = 08) x3 + 3 x2 x 3 = 0-1- o N2U0n1E24 lKju3t9aL BS5oRfetUwEaxrpeU V CAulZlF br4iTgCh9tNsU w EMRaFdgeu TwmiHt0hZ HIAnxfPiUnxiptwee 5 AulbgDelbvrbae by Kuta Software LLC9) x3 2 x2 3 x + 6 = 010) x6 2 x4 4 x2 + 8 = 011) x5 + 2 x4 + 11 x3 + 22 x2 + 24 x + 48 = 012) x6 + 5 x4 4 x2 20 = 013) x6 x4 x2 + 1 = 014)

2 X8 26 x4 + 25 = 0-2- o 9240S1Y2F pK5uTtnaS xSVoOfTt7wta8rAeh B 2 ANl7ls irVingGhVtIsw V WMkahdTeO RwzixtZhr II4nqfQi1nDiAtzeW JAVlkgjetbBrVaw by Kuta Software LLCKuta Software - Infinite Algebra 2 Name_____ Period____Date_____Analyzing and Solving Polynomial EquationsState the number of complex roots, the possible number of real and imaginary roots, the possiblenumber of positive and negative roots, and the possible rational roots for each equation. Then find ) x4 5 x2 36 = 0# of complex roots: 4 Possible # of real roots: 4, 2, or 0 Possible # of imaginary roots: 4, 2, or 0 Possible # positive real roots: 1 Possible # negative real roots: 1 Possible rational roots: 1, 2, 3, 4, 6, 9, 12, 18, 36 Roots: {2i, 2i, 3, 3}2) x3 + 3 x2 14 x 20 = 0# of complex roots: 3 Possible # of real roots: 3 or 1 Possible # of imaginary roots: 2 or 0 Possible # positive real roots: 1 Possible # negative real roots: 2 or 0 Possible rational roots: 1, 2, 4, 5, 10, 20 Roots: { 5, 1 + 5, 1 5}3) x3 2 x2 + 3 x 6 = 0# of complex roots: 3 Possible # of real roots.

3 3 or 1 Possible # of imaginary roots: 2 or 0 Possible # positive real roots: 3 or 1 Possible # negative real roots: 0 Possible rational roots: 1, 2, 3, 6 Roots: {2, i3, i3}4) x4 14 x2 + 45 = 0# of complex roots: 4 Possible # of real roots: 4, 2, or 0 Possible # of imaginary roots: 4, 2, or 0 Possible # positive real roots: 2 or 0 Possible # negative real roots: 2 or 0 Possible rational roots: 1, 3, 5, 9, 15, 45 Roots: {5, 5, 3, 3}5) x4 + 6 x2 + 8 = 0# of complex roots: 4 Possible # of real roots: 4, 2, or 0 Possible # of imaginary roots: 4, 2, or 0 Possible # positive real roots: 0 Possible # negative real roots: 0 Possible rational roots: 1, 2, 4, 8 Roots: {2i, 2i, i2, i2}6) x4 + 3 x2 18 = 0# of complex roots: 4 Possible # of real roots: 4, 2, or 0 Possible # of imaginary roots: 4, 2, or 0 Possible # positive real roots: 1 Possible # negative real roots: 1 Possible rational roots: 1, 2, 3, 6, 9, 18 Roots: {3, 3, i6, i6}7) x3 1 = 0# of complex roots: 3 Possible # of real roots: 3 or 1 Possible # of imaginary roots: 2 or 0 Possible # positive real roots: 1 Possible # negative real roots: 0 Possible rational roots: 1 Roots: {1, 1 + i32, 1 i32}8) x3 + 3 x2 x 3 = 0# of complex roots.

4 3 Possible # of real roots: 3 or 1 Possible # of imaginary roots: 2 or 0 Possible # positive real roots: 1 Possible # negative real roots: 2 or 0 Possible rational roots: 1, 3 Roots: { 3, 1, 1}-1- K 22103172w 4 KVu4txaZ mSiohfQttwEaNr5em o qAalklJ 7r1iDgIhztTsx F TMSa1dFeq 7wLiwtIh2 RIOngfPiAn3i7tae4 wAIlGgGeMbMrIab by Kuta Software LLC9) x3 2 x2 3 x + 6 = 0# of complex roots: 3 Possible # of real roots: 3 or 1 Possible # of imaginary roots: 2 or 0 Possible # positive real roots: 2 or 0 Possible # negative real roots: 1 Possible rational roots: 1, 2, 3, 6 Roots: {2, 3, 3}10) x6 2 x4 4 x2 + 8 = 0# of complex roots: 6 Possible # of real roots: 6, 4, 2, or 0 Possible # of imaginary roots: 6, 4, 2, or 0 Possible # positive real roots: 2 or 0 Possible # negative real roots: 2 or 0 Possible rational roots: 1, 2, 4, 8 Roots: {2 mult.}

5 2, 2 mult. 2, i2, i2}11) x5 + 2 x4 + 11 x3 + 22 x2 + 24 x + 48 = 0# of complex roots: 5 Possible # of real roots: 5, 3, or 1 Possible # of imaginary roots: 4, 2, or 0 Possible # positive real roots: 0 Possible # negative real roots: 5, 3, or 1 Possible rational roots: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Roots: { 2, i3, i3, 2i2, 2i2}12) x6 + 5 x4 4 x2 20 = 0# of complex roots: 6 Possible # of real roots: 6, 4, 2, or 0 Possible # of imaginary roots: 6, 4, 2, or 0 Possible # positive real roots: 1 Possible # negative real roots: 1 Possible rational roots: 1, 2, 4, 5, 10, 20 Roots: { i5, i5, 2, 2, i2, i2}13) x6 x4 x2 + 1 = 0# of complex roots: 6 Possible # of real roots: 6, 4, 2, or 0 Possible # of imaginary roots: 6, 4, 2, or 0 Possible # positive real roots: 2 or 0 Possible # negative real roots: 2 or 0 Possible rational roots: 1 Roots: {1 mult.

6 2, 1 mult. 2, i, i}14) x8 26 x4 + 25 = 0# of complex roots: 8 Possible # of real roots: 8, 6, 4, 2, or 0 Possible # of imaginary roots: 8, 6, 4, 2, or 0 Possible # positive real roots: 2 or 0 Possible # negative real roots: 2 or 0 Possible rational roots: 1, 5, 25 Roots: {1, 1, i, i, 5, 5, i5, i5}-2-Create your own worksheets like this one with Infinite Algebra 2. Free trial available at