Find all the root/s for the polynomial equation x 3 -3x 2 -5x+15=0.

{ 3 , ± 5 } \left\{3,\ \pm\sqrt{5}\right\} { 3 , ± 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

{ 3 , 5 } \left\{3,\ \sqrt{5}\right\} { 3 , 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

{ − 3 , ± 5 } \left\{-3,\ \pm\sqrt{5}\right\} { − 3 , ± 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

{ 3 , ± 5 i } \left\{3,\ \pm5i\right\} { 3 , ± 5 i }

Solve: -6x-1+5x 2 =8x 2

x = − 3 ± 6 3 x=\frac{-3\pm\sqrt{6}}{3} x = 3 − 3 ± 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = 5 ± 67 6 x=5\pm\frac{\sqrt{67}}{6} x = 5 ± 6 6 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = 1 ± 22 x=1\pm\sqrt{22} x = 1 ± 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = 1 , 2 7 x=1,\ \frac{2}{7} x = 1 , 7 2

Find the real or imaginary solutions to x 4 =13x 2 -36.

x = ± 3 , ± 2 x=\pm3,\ \pm2 x = ± 3 , ± 2

x = ± 9 , ± 4 x=\pm9,\ \pm4 x = ± 9 , ± 4

x = 9 , 4 , 3 , 2 x=9,\ 4,\ 3,\ 2 x = 9 , 4 , 3 , 2

Solve x 3 +5x 2 -6x-30=0.

{ − 5 , ± 6 } \left\{-5,\ \pm\sqrt{6}\right\} { − 5 , ± 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

{ 5 , ± 6 } \left\{5,\ \pm6\right\} { 5 , ± 6 }

{ − 5 ± 6 } \left\{-5\pm6\right\} { − 5 ± 6 }

{ − 5 ± 6 } \left\{-5\pm\sqrt{6}\right\} { − 5 ± 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

Solve: x 4 +2x 3 -8x-16=0

{ ± 2 , − 1 ± i 3 } \left\{\pm2,\ -1\pm i\sqrt{3}\right\} { ± 2 , − 1 ± i 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

x = ± 2 , ± 3 x=\pm2,\ \pm\sqrt{3} x = ± 2 , ± 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

{ ± 2 , − 1 ± 3 } \left\{\pm2,\ -1\pm\sqrt{3}\right\} { ± 2 , − 1 ± 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> }

x = ± 2 , ± 3 i x=\pm2,\ \pm\sqrt{3}i x = ± 2 , ± 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i

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SOLVING POLYNOMIAL EQUATIONS

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Mathematics

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10th Grade

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Practice Problem

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Hard

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CCSS

HSA-REI.B.4B, HSA.APR.B.3, HSA.APR.B.2

Standards-aligned

Christian Flaviano

Used 59+ times

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20 questions

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MULTIPLE SELECT QUESTION

1 min • 1 pt

How many root/s does the polynomial equation have?
x⁴-3x²+10=0

MULTIPLE SELECT QUESTION

1 min • 1 pt

How many solution/s does the polynomial equation have?
5x³-10x²+8x+1=0

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Write a polynomial equation of least degree that has a leading coefficient of 1 and zeros at 1, 4, and -2.

(x-1)(x-4)(x+2)=0

(x+1)(x+4)(x-2)=0

x³+3x²+6x+8=0

x³-3x²-6x+8=0

Which of the following is a COMPLETE list of all possible roots?
$x^3+5x^2-9x+5=0$

1 and 5

-1 and -5

1, -1, 5, and -5

1, -1, 5, -5, 1/5, and -1/5

MULTIPLE SELECT QUESTION

1 min • 1 pt

Is (x+5) a factor of x³+2x²-x+4=0?

YES

Solve: x²+7x+6=0

{-6, -1}

{2, -3}

{6, 1}

{-2, 3}

State the leading term of the polynomial, 6x⁵+9x⁴+2x³+3x²-4x-6=0.

x⁵

6x⁵

9x⁴

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SOLVING POLYNOMIAL EQUATIONS

20 questions

How many root/s does the polynomial equation have?
x⁴-3x²+10=0

How many solution/s does the polynomial equation have?
5x³-10x²+8x+1=0

Write a polynomial equation of least degree that has a leading coefficient of 1 and zeros at 1, 4, and -2.

Which of the following is a COMPLETE list of all possible roots?
$x^3+5x^2-9x+5=0$

Is (x+5) a factor of x³+2x²-x+4=0?

Solve: x²+7x+6=0

State the leading term of the polynomial, 6x⁵+9x⁴+2x³+3x²-4x-6=0.

Solve the equation. x⁴+4x³+3x²=0

Below are four possible zeros for this polynomial.
x³+2x²-11x-12=0
Figure out which one works.

Solve for the value of x:
(2x+5)(5x-2)=0

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

SOLVING POLYNOMIAL EQUATIONS

20 questions

How many root/s does the polynomial equation have?x4-3x2+10=0

How many solution/s does the polynomial equation have?5x3-10x2+8x+1=0

Write a polynomial equation of least degree that has a leading coefficient of 1 and zeros at 1, 4, and -2.

Which of the following is a COMPLETE list of all possible roots? x3+5x2−9x+5=0x^3+5x^2-9x+5=0x3+5x2−9x+5=0

Is (x+5) a factor of x3+2x2-x+4=0?

Solve: x2+7x+6=0

State the leading term of the polynomial, 6x5+9x4+2x3+3x2-4x-6=0.

Solve the equation. x4+4x3+3x2=0

Below are four possible zeros for this polynomial. x3+2x2-11x-12=0Figure out which one works.

Solve for the value of x:(2x+5)(5x-2)=0

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

How many root/s does the polynomial equation have?
x⁴-3x²+10=0

How many solution/s does the polynomial equation have?
5x³-10x²+8x+1=0

Which of the following is a COMPLETE list of all possible roots?
$x^3+5x^2-9x+5=0$

Is (x+5) a factor of x³+2x²-x+4=0?

Solve: x²+7x+6=0

State the leading term of the polynomial, 6x⁵+9x⁴+2x³+3x²-4x-6=0.

Solve the equation. x⁴+4x³+3x²=0

Below are four possible zeros for this polynomial.
x³+2x²-11x-12=0
Figure out which one works.

Solve for the value of x:
(2x+5)(5x-2)=0