Question

Solve for the roots of x in each of the equations below.

x^4 - 81 = 0
x^4 + 10x^2 + 25 = 0
x^4 - x^2 - 6 = 0

Answer 1

what number squared is 81?

Answer 2

3, -3, 3i, -3i

Answer 3

@rkopen

Answer 4

@e.mccormick

Answer 5

@SolomonZelman

Answer 6

For question 1. \(\Large\color{black}{ \bf hint.~~~81=3^4 }\)

For question 2. Let x^2=a, and complete the square.

For question 3. Let x^2=a and factor.

Answer 7

for 1 i have 3,-3,3i,-3i

Answer 8

For 2 I have, 5,-5,5i,-5i

Answer 9

hello

Answer 10

I was out for a little, sorry about that.

1) Correct

2)
\(\normalsize\color{black}{ \ x^4 + 10x^2 + 25 = 0 ~~~~~~~~~~let~~x^2=a }\)
\(\normalsize\color{black}{ \ a^2 + 10a + 25 = 0 }\)
\(\normalsize\color{black}{ \ (a+5)^2 = 0 }\)
\(\normalsize\color{black}{ \ a+5 = 0 }\)
\(\normalsize\color{black}{ \ a = -5 ~~~~~~~~~x^2=-5 }\)
\(\normalsize\color{black}{ \ Hence,~~~~~ x = ±5i }\)
-5 is not one of the x solutions.

Answer 11

I mean +5 is not... -5 is correct.

So 2) real root -5 imaginary roots +5i, -5i

Answer 12

For number 3,

\(\normalsize\color{blue}{ \ x^4 - x^2 - 6 = 0~~~~~~~~~~~~~let~~x^2=a}\)
\(\normalsize\color{blue}{ \ a^2 - a - 6 = 0~~~~~~~~~~~~~~~factor,}\)
\(\normalsize\color{blue}{ \ (a-3)(a+2) = 0}\)
\(\normalsize\color{blue}{ \ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Hence,~~~~ a=3,-2}\)
\(\normalsize\color{blue}{ \ a=3,-2~~~~thus~}\)
\(\normalsize\color{blue}{ \ x^2=3~~~~~~and~~~~~~x^2=-3}\)
\(\normalsize\color{blue}{ \ x=± ~3~~~~~~and~~~~~~x=±~3i}\)

Answer 13

3,-2,-3,+/-3,+/-3i or

3,-3, +/-3, +/-3i

Answer 14

\(\normalsize\color{blue}{ \ x^2=3~~~~~~and~~~~~~x^2=-2}\)
\(\normalsize\color{blue}{ \ x=± \sqrt{3}~~~~~~and~~~~~~x=±~2i}\)

Answer 15

That is what I meant.