We need to solve this equation: x^{4} - x^{3} + 4x^{2} - 16x - 192 =0

Zoe Oneal

Zoe Oneal

Answered question

2020-12-13

We need to solve this equation:
x4x3+4x216x192=0

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2020-12-14Added 109 answers

Use the rational root theorem, a0=192 and
an=1.
The divider of a0is1,2,3,4,6,8,12,16,24,32,48,96,192.
Rational Zero =±1,2,3,4,6,8,12,16,24,32,48,96,1921
The root of the equation is - 3 by trial and error method then, the factor is x+3. Now, divide the provided equation with calculated factor.
x4x3+4x216x192=x4x3+4x216x192x+3
=(x+3)(x34x2+16x64)
Now, further factorize the above equation.
(x+3)(x34x2+16x64)=0
(x+3)((x34x2)+(16x64))=0
(x+3)(x2(x4)+16(x4))=0
(x+3)(x4)(x2+16)=0
x=3,4,±4i
Answer: Therefore, the real solution of the provided equation is x=3,4.

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