Show the work steps for finding the roots of x^{4}-13x^{2}+36

Juan Hewlett

Juan Hewlett

Answered question

2021-12-29

Show the work steps for finding the roots of x413x2+36 algebraically.

Answer & Explanation

sukljama2

sukljama2

Beginner2021-12-30Added 32 answers

We finding the roots of x413x2+36
Now x413x2+36
=x49x24x2+36
=x2(x29)4(x29)
=(x29)(x24)
[a2b2=(a+b)(ab)
=(x232)(x222)
=(x+3)(x3)(x+2)(x2)
For the roots of x413x2+36
x413x2+36=0
(x+3)(x3)(x+2)(x2)=0
either x+3=0
x=3
x3=0
x=3
x+2=0
x=2
x2=0
x=2
Hence x=3,2,2,3
Janet Young

Janet Young

Beginner2021-12-31Added 32 answers

x413x2+36
(x3)(x3+3x24x12)
(x3)(x2)(x2+5x+6)
(x3)(x2)(x+2)(x+3)
karton

karton

Expert2022-01-04Added 613 answers

Given:
x413x2+36t213t+36=0D=169144=25=52t1,2=13+52t1=9t2=4x2=9x=3x=3x2=4x=2x=2Answer: x=2,x=2,x=3,x=3

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