Find the value of `x^4+9x^3+35 x^2-x+4` for `x=-5+2sqrt(-4).`

Answer

`-160`

Explanation

we have,
`x = -5 + 4i`
`or (x+5)^(2) =- 16`
`or x^(2) + 10 x + 41 = 0`
Now, `x^(4) + 9x^(3) +35x^(2) - x +4`
`= x^(2)(x^(2)+10x+41)-x(x^(2)+10x + 41) + 4(x^(2) + 10 + 41) - 160`
`=0x^(2) = 0x + 4 xx 0 - 160=-160" "["Using(1)"]`