If x-5-4- find the value of x4-9 x3-35 x2-x-4

X= 5+√( 4), ∴ x +5 =4i ⇒ (x+5)^2= 16 ⇒ x^2+25+10x = 16 ⇒ x^2+0x +41 =0 Now we may write x^4 +9x^3+35x^2 x+4 =x^2(x^2+10x+41) x(x^2+10x+41)+4(x^2+10x+41) 160 =( ...

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Byju's Answer

Standard XII

Mathematics

Definition of Relations

If x=-5+√-4, ...

Question

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

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Solution

$x = - 5 + \sqrt{- 4}, ∴ x + 5 = 4 i \Rightarrow (x + 5)^{2} = - 16 \Rightarrow x^{2} + 25 + 10 x = - 16 \Rightarrow x^{2} + 0 x + 41 = 0$
Now we may write $x^{4} + 9 x^{3} + 35 x^{2} - x + 4$
$= x^{2} (x^{2} + 10 x + 41) - x (x^{2} + 10 x + 41) + 4 (x^{2} + 10 x + 41) - 160 = (x^{2} \times 0) - (x \times 0) + (4 \times 0) - 160 = - 160$

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If x=−5+√−4, find the value of x4+9x3+35x2−x+4.

x=−5+√−4,∴x+5=4i⇒(x+5)2=−16⇒x2+25+10x=−16⇒x2+0x+41=0 Now we may write x4+9x3+35x2−x+4 =x2(x2+10x+41)−x(x2+10x+41)+4(x2+10x+41)−160=(x2×0)−(x×0)+(4×0)−160=−160

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