CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Strictly Increasing Functions

Evaluate the ...

Question

Evaluate the mentioned below:

(v) $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41, w h e n x = - 2 - \sqrt{3} i$

Open in App

Solution

Given that-
$x = - 2 - \sqrt{3} i$
$\Rightarrow x + 2 = - \sqrt{3} i$
$\Rightarrow (x + 2)^{2} = (- \sqrt{3} i)^{2} s q u a r i n g o n b o t h s i d e$
$\Rightarrow x^{2} + 4 x + 7 = 0 \dots (1)$
$\Rightarrow 2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41$
$= 2 x^{2} (x^{2} + 4 x + 7) - 3 x^{3} - 7 x^{2} - x + 41$
$= 2 x^{2} (x^{2} + 4 x + 7) - 3 x (x^{2} + 4 x + 7) + 5 x^{2} + 20 x + 41$
$= 2 x^{2} (x^{2} + 4 x + 7) - 3 x (x^{2} + 4 x + 7) + 5 (x^{2} + 4 x + 7) + 6$
$= 2 x^{2} \times 0 - 3 x \times 0 + 5 \times 0 + 6 f r o m e q n (1)$
=6
Therefore, $2 x^{4} + 5 x^{3} + 7 x^{2} - x + 41 = 6$

Suggest Corrections

thumbs-up

1

Similar questions

Q. Evaluate the mentioned below:
(iv)

x^{6} + x^{4} + x^{2} + 1, w h e n x = (1 + i) / \sqrt{2}

Q. Evaluate the mentioned below:
(iii)

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 9, w h e n x = - 1 + i \sqrt{2}

x^{2} - y^{2}

) × (𝑥 – 𝑦) = ______.

Q. Evaluate the mentioned below
(ii)

x^{4} - 4 x^{3} + 4 x^{2} + 8 x + 44, w h e n x = 3 + 2 i

Q. Evaluate the mentioned below:
(i)

2 x^{3} + 2 x^{2} - 7 x + 72, w h e n x = \frac{3 - 5 i}{2}

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Strictly Increasing Functions

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon