AnswersAlgebra 2Solving Polynomial Equations with Complex Solutions

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Find all solutions to the equation 3 x cubed plus 12 x is equal to 2 x squared plus 8

A
negative 2 comma negative 2 thirds comma 2
B
2 thirds comma negative 2 i comma 2 i
C
negative 2 comma 2 thirds comma 2
D
negative 2 thirds comma negative 2 i comma 2 i
2
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Consider the equation 3 x cubed plus 14 x squared minus 14 x plus 60 is equal to 0 The real solution is negative 6 What are the nonreal solutions?

A
4 minus 2 i square root of 26 comma 4 plus 2 i square root of 26
B
negative 2 i square root of 26 comma 2 i square root of 26
C
the fraction with numerator negative 2 plus i square root of 26 and denominator 3 comma the fraction with numerator negative 2 minus i square root of 26 and denominator 3
D
the fraction with numerator 2 plus i square root of 26 and denominator 3 comma the fraction with numerator 2 minus i square root of 26 and denominator 3
3

Find all the solutions to 3 x cubed minus 6 x squared plus 30 x minus 20 is equal to negative 20

A
0 comma 2 plus 6 i comma 2 minus 6 i
B
0 comma negative 1 plus 3 i comma negative 1 minus 3 i
C
0 comma negative 2 plus 6 i comma negative 2 minus 6 i
D
0 comma 1 plus 3 i comma 1 minus 3 i
4

What are the solutions to negative 24 x minus 24 is equal to x cubed plus 8 x squared ?

A
negative 1 comma negative 3 plus i square root of 3 comma negative 3 minus i square root of 3
B
negative 2 comma negative 3 plus i square root of 3 comma negative 3 minus i square root of 3
C
2 comma 3 plus i square root of 3 comma 3 minus i square root of 3
D
1 comma 3 plus i square root of 3 comma 3 minus i square root of 3
5

There is one negative solution and two nonreal solutions to the equation x cubed plus 87 is equal to 7 x squared plus x What are the solutions?

A
negative 3 comma 5 plus 2 i comma 5 minus 2 i
B
3 comma 5 plus 2 i comma 5 minus 2 i
C
negative 3 comma negative 5 plus 2 i comma negative 5 minus 2 i
D
3 comma negative 5 plus 2 i comma negative 5 minus 2 i
6

What are all the solutions to the equation 10 x to the 4th power plus 30 x cubed plus 35 x squared is equal to 0 ?

A
0 comma 6 plus 2 i square root of 5 comma 6 minus 2 i square root of 5
B
0 comma the fraction with numerator negative 3 plus i square root of 5 and denominator 2 comma the fraction with numerator negative 3 minus i square root of 5 and denominator 2
C
0 comma the fraction with numerator 3 plus i square root of 5 and denominator 2 comma the fraction with numerator 3 minus i square root of 5 and denominator 2
D
0 comma negative 6 plus 2 i square root of 5 comma negative 6 minus 2 i square root of 5
7

If the real roots of the equation 3 x to the 4th power minus 6 x cubed plus 3 x squared minus 54 x minus 216 is equal to 0 are negative 2 and 4 , what are the nonreal roots?

A
negative 9 i comma 9 i
B
negative 3 i comma 3 i
C
negative 6 i square root of 6 comma 6 i square root of 6
D
negative 3 i square root of 3 comma 3 i square root of 3
8

Find all the solutions to the equation 4 x cubed plus 16 x squared plus 28 x is equal to 0

A
0 comma 4 plus 2 i square root of 3 comma 4 minus 2 i square root of 3
B
0 comma negative 2 plus i square root of 3 comma negative 2 minus i square root of 3
C
0 comma 2 plus i square root of 3 comma 2 minus i square root of 3
D
0 comma negative 4 plus 2 i square root of 3 comma negative 4 minus 2 i square root of 3
9

The real root of the equation x cubed minus 7 x squared plus 15 x minus 25 is equal to 0 is 5 What are the nonreal roots?

A
1 plus 2 i comma 1 minus 2 i
B
negative 16 i comma 16 i
C
2 minus 4 i comma 2 plus 4 i
D
negative 4 i comma 4 i
10

Consider the equation 4 x to the 4th power minus 8 x cubed plus 4 x squared minus 128 x minus 960 is equal to 0 The real solutions are 5 and negative 3 What are the nonreal solutions?

A
negative 16 i comma 16 i
B
negative 2 i comma 2 i
C
negative 4 i comma 4 i
D
negative 8 i comma 8 i

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