If x = - 5 + 2√ { - 4} , then value of expression {x^4} + 9{x^3} + 35{x^2} - x + 4 is

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4-1.Complex numbers

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

A

$160$

B

$- 160$

C

$60$

D

$- 60$

(IIT-1972)

Solution

(b)$x + 5 = 4i$==> ${x^2} + 10x + 25 = – 16$
Now, ${x^4} + 9{x^3} + 35{x^2} – x + 4$
$ = ({x^2} + 10x + 41)({x^2} – x + 4) – 160 = – 160$

Standard 11

Mathematics

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