Question

If $x=-5+2\sqrt{-4},$ find the value of $x^4+9x^3+35x^2-x+4.$

• A. $-160.$
• B. $-80.$
• C. $160.$
• D. $80.$

Answer 1

The correct option is A $-160.$

We have, $x+5=2\sqrt{-4}.$

Squaring, $x^2+10x+25=-16$

or $x^2+10x+41=0$ ...(1)

divide $x^4+9x^3+35x^2-x+4$ by $x^2+10x+41$

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

Above statement is dividend $=$ divisor $\times$ quotient $+$ remainder

where dividend $=x^4+9x^3+35x^2-x+4$

divisor $=x^2+10x+41$

By 1 now put $x^2+10x+41=0$

$\therefore$ Value of $x^4+9x^3+35x^2-x+4=-160.$

Ans: A