Question

If x=-5+4i find the value of x^(4)+9x^(3)+35x^(2)-x+64​

Answer 1

Answer:

ANSWER

Given:f(x)=x

4

+9x

3

+35x

2

−x+4

if x=−5+4i

⇒(x+5)=4i

⇒(x+5)

2

=(4i)

2

⇒x

2

+25+10x=−16

⇒x

2

+10x+41=0−(i)

All we have to do is divide the expression x

4

+9x

3

+35x

2

−x+4 by x

2

+10x+41 via the long division method.

∴x

4

+9x

3

+35x

2

−x+4=(x

2

+10x+41)(x

2

−x+4)−160

∴f(x)=x

4

+9x

3

+35x

2

−x+4=−160

please follow me