Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 7-12-2020

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Loading DoubtNut Solution for you

Watch 1000+ concepts & tricky questions explained!

195.2 K+

120.7 K+

Text Solution

Solution :

Let `P(x) = x^3+ax^2+bx+c`<br>
Then, `P(1) = 1+a+b+c = 1`<br>
`=> a+b+c = 0->(1)`<br>
`P(2) = 8+4a+2b+c = 2=> 4a+2b+c = -6->(2)`<br>
`P(3) = 27+9a+3b+c = 3=>9a+3b+c = -24->(3)`<br>
Subtracting (1) from (2)<br>
`3a+b = -6->(4)`<br>
Subtracting (2) from (3)<br>
`5a+b = -18->(5)`<br>
Subtracting (4) from (5)<br>
`2a = -12 => a = -6`<br>
`=> b = -6+18 = 12`<br>
`c = -a-b = 6-12 = -6`<br>
So, our polynomial becomes,<br>
`P(x) = x^3-6x^2+12x-6 = 0`<br>
`:.P(4) = 64-96+48-6 = 10`<br>
**Definition of algebraic expressions**

**Operations on algebric expressions - Addition, Subtraction, Multiplication and Division**

**Some Important Identities - (i) `(a+b)^2 = a^2 + 2ab + b^2` (ii) `(a-b)^2 = a^2 - 2ab + b^2`**

**Important Identity - `(a-b)(a+b) = a^2 - b^2`**

**Important Identitiy `(x+a)(x+b) = x^2+(a+b)x+ab`**

**Expand each of the following (i) `(2x+5y)^2` (ii) `(x-3y)^2` (iii) `(x+5)(x-3)`**

**Evaluate each of the following by using Identities - (i) 103 x 97 (ii) 103 x 103 (iii) 97 x 97 (iv) 105 + 106**

**Simplify : `(a-1/a)(a+1/a)(a^2+1/a^2)(a^4+1/a^4)(a^8+1/a^8)`**

**If `x+1/x = 4`; Find (i) `x^2+1/x^2` (ii) `x^4 + 1/x^4`**

**If `x^2+1/x^2` = 5 is given then find the value of (i) `x+1/x` (ii) ` x-1/x`**