Question

x^4+9x^3+35x^2-x+4,if x=-5+√-4​

Answer 1

Answer:

Step-by-step explanation:

You could consider carrying out polynomial long division, dividing the given polynomial by the minimal polynomial of (−5 + 4i), which is x² + 10x + 41. Viz:

x⁴ +9x³ + 35x² − x + 4

= ( x² − x − 4 ) ( x² + 10x + 41 ) + 160

We know that if x = −5 + 4i, then x² + 10x + 41 vanishes, so the given polynomial evaluates to 160 there.

Answer 2

Step-by-step explanation:

Given,

x=-5+4i

x+5=4i

S.O.B.S

(x+5)^2=(4i)^2

x^2+25+10x=-16

Now,

Divide x^4+9x^3+35x^2-x+4 by x^2+25+10x=-16

By long division method,

x^4+9x^3+35x^2-x+4=(x^2+10x+41)(x^2-x+4)-160

hence,

f(x)=x^4+9x^3+35x^2-x+4=-160