Question

উৎপাদকে বিশ্লেষন করো x4+x2+1
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Answer 1

Step-by-step explanation:

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x*4+x²+1

x².x²+x².1+1

x²(x²+1)+1=0

x²+1=0

x²=-1

x=1

Answer 2

Step-by-step explanation:

x4+x2+1=x4+x3+x2−x3−x2−x+x2+x+1

=>x2(x2+x+1)−x(x2+x+1)+(x2+x+1)

=>(x2+x+1)∗(x2−x+1)

Approach # 2:

Let y=x2

=>x4+x2+1=y2+y+1

Let us find the roots

y2+y+1=0

=>y=−1±1–4√2

=>y=12∗(−1±3–√i)

=>y=x2=12∗(−1±3–√i)

x2=[12∗(−1±3–√i)]2

=>x=±[12∗(−1±3–√i)]

The 4 roots are

R1=+[12∗(−1+3–√i)]

R2=+[12∗(−1−3–√i)]

R3=−[12∗(−1+3–√i)]

R4=−[12∗(−1−3–√i)]

(x−R1),(x−R2),(x−R3),(x−R4) are the factors