If x - - 2 - -3- find the value of 2x4 - 5x3 - 7x2 - x - 41-

x= 2 √( 3) ⇒ x+2= √( 3) on squaring, we get ⇒ x ^ 2 +4+4x= 3 ⇒ x ^ 2 +4x+7=0 #160; #160; #160; #160; #160;...(1)Dividing ...

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Byju's Answer

Standard XII

Mathematics

How to Find the Inverse of a Function

If x = - 2 ...

Question

If $x = - 2 - \sqrt{- 3}$ , find the value of $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41$ .

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Solution

$x = - 2 - \sqrt{- 3}$
$\Rightarrow x + 2 = - \sqrt{- 3}$
on squaring, we get $\Rightarrow x^{2} + 4 + 4 x = - 3$
$\Rightarrow x^{2} + 4 x + 7 = 0$ ...(1)
Dividing $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41$ with $x^{2} + 4 x + 7$ , we get
$2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41 = (x^{2} + 4 x + 7) (2 x^{2} - 3 x + 5) + 6$
Therefore using (1), we get $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41 = 6$
Ans: 6

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Similar questions

Q. The value of

2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41

, when

x = - 2 - \sqrt{3 i}

is:

Q. Evaluate the following:
(i)

2 x^{3} + 2 x^{2} - 7 x + 72, when x = \frac{3 - 5 i}{2}

(ii)

x^{4} - 4 x^{3} + 4 x^{2} + 8 x + 44, when x = 3 + 2 i

(iii)

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 9, when x = - 1 + i \sqrt{2}

(iv)

x^{6} + x^{4} + x^{2} + 1, when x = \frac{1 + i}{\sqrt{2}}

(v)

2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41, when x = - 2 - \sqrt{3} i

Evaluate the following :

$(i) 2 x^{3} + 2 x^{2} - 7 x + 72, w h e n x = \frac{3 - 5 i}{2} (i i) x^{4} - 4 x^{3} + 4 x^{2} + 8 x + 44, w h e n x = 3 + 2 i (i i i) x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 9, w h e n x = - 1 + i \sqrt{2} (i v) x^{6} + x^{4} + x^{2} + 1, w h e n x = \frac{1 + i}{\sqrt{2}} (v) 2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41, w h e n x = - 2 - \sqrt{3} i$

Q. If

2 x^{4} - 5 x^{3} + 2 x^{2} - x + a

is exactly divisible by

x^{2} - 3 x + 2

. Find

a

Q. Find the value of a such that (x − 4) is a factors of 5x³ − 7x² − ax − 28.

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If x=−2−√−3, find the value of 2x4+5x3+7x2−x+41.

x=−2−√−3⇒x+2=−√−3on squaring, we get ⇒x2+4+4x=−3⇒x2+4x+7=0 ...(1)Dividing 2x4+5x3+7x2−x+41 with x2+4x+7, we get2x4+5x3+7x2−x+41=(x2+4x+7)(2x2−3x+5)+6Therefore using (1), we get 2x4+5x3+7x2−x+41=6 Ans: 6

If $x = - 2 - \sqrt{- 3}$ , find the value of $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41$ .