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find the value of x 4 + 4x 3 +6x 2 -8x+4 for x= -2+2*root(-4) is -20 20 16 -60

find the value  of
 
x4 +  4x3+6x2-8x+4 for x= -2+2*root(-4) is
  1. -20
  2. 20
  3. 16
  4. -60
 

Grade:12

1 Answers

jagdish singh singh
173 Points
8 years ago
\hspace{-0.7 cm }$ Given $\bf{f(x) =x^4 + 4x^3+6x^2-8x+4.}$ Now we have to calculate \\\\of $\bf{f(x)}$ at $\bf{ x= -2+2\sqrt{-4} = -2+4i.\;, }$ Where $\bf{i=\sqrt{-1}}$ and $\bf{i^2=-1}$\\\\ So Here $\bf{x=-2+4i\Rightarrow (x+2)^2=(4i)^2\Rightarrow x^2+4+4x=16i^2}$\\\\ So we get $\bf{x^2+4+4x=-16.\Rightarrow x^2+4x+20 =0}$\\\\ So we can write $\bf{f(x)= x^2\cdot (x^2+4x+20)-14x^2-8x+4}$\\\\ So $\bf{f(x)=x^2(0)-14(x^2+4x+20)+48x+284}=48x+284$

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