Download App

Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers4 Marks
Question
Evaluate the following:
$2\text{x}^3+2\text{x}^2-7\text{x}+72,$ when $\text{x}=\frac{3-5\text{i}}{2}$
✓

Answer

$\text{x}=\frac{3-5\text{i}}{2}$
$\Rightarrow2\text{x}=3-5\text{i}$
$\Rightarrow2\text{x}-3=-5\text{i}$
$\Rightarrow(2\text{x}-3)^2=(-5\text{i})^2$
$\Rightarrow4\text{x}^2+9-12\text{x}=-25$
$\Rightarrow4\text{x}^2-12\text{x}+34=0$
$\Rightarrow2(2\text{x}^2-6\text{x}+17)=0$
$\Rightarrow2\text{x}^2-6\text{x}+17=0 \ ...(\text{i})$
$\therefore2\text{x}^3+2\text{x}^2-7\text{x}+72$
$=\text{x}(2\text{x}^2-6\text{x}+17)+6\text{x}^2-17\text{x}+2\text{x}^2-7\text{x}+72$ (Adding and subtracting $6x^2$ and $17x$)
$\text{x}\times0+8\text{x}^2-24\text{x}+72$ (Using(i))
$=4(2\text{x}^2-6\text{x}+17)+4$
$=4\times0+4$ (Using(i))
$=4$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(4 Marks)" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that,

(a) number on the ticket is divisible by 6.

(b)the number on the ticket is a perfect square.

(c)the number on the ticket is prime.

(d)the number on the ticket is divisible by 3 and 5.

→
In a G.P. the $3^{rd}$​​​​​​​ term is $24$ and the 6th term is $192$. Find the $10\ th$ term.
→
$\frac{\tan ^2 x}{1+\tan ^2 x}+\frac{\cot ^3 x}{1+\cot ^2 x}=\sec x \operatorname{cosec} x-2 \sin x \cos x$
→
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when
1. $n = 10$
2. $n = 15$
3. $n = 12$
4. $n = 8$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin(\text{a}+\text{x})+\sin(\text{a}-\text{x})-2\sin\text{a}}{\text{x}\sin\text{x}}$
→
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
→
For any two sets of A and B, prove that:$\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$
→
Prove that the perpendicular drawn from the point (4, 1) on the join of (2, -1) and (6, 5) divides it in the ratio 5:8.
→
Solve the following equations:
$\tan\text{x}+\tan2\text{x}+\tan3\text{x}=0$
→
From 4 officers and 8 jawans in how many ways can 6 be chosen:
  1. To include exactly one officer.
  2. To include at least one officer?
→