Question

Find the value of a and b so that the polynomial x
- 4x2 + ax + b is exactly divisible by X-2 as well
as x + 1.
[4]





TRASH ANSWERS WILL NOT BE TOLERATED!!​

Answer 1

☛ Given :

Polynomial expression

$x - 4 {x}^{2} + ax + b$

(x - 2) & (x + 1) are exactly divisible .

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⭐ Required to find :

1. Values of " a " and " b "

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✯ Explanation :

What is a polynomial ?

In mathematics ; a polynomial is an expression which consists of variables , coefficient separated by mathematical functions such as addition , subtraction , multiplication with non - negative integral powers .

Example :

$2{x}^{2} + x + 3$

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⚝ Solution :

Given :

p(x) = x - 4x^2 + ax + b

(x-2) is divisible

Let, x - 2 = 0

$\boxed{ x = 2 }$

Hence,

Substitute this value in place of x

We get ;

p(2) = (2) - 4(2)^2 + a(2) + b

==>. 2 - 4(4) + 2a + b = 0

==>. 2 - 16 + 2a + b = 0

==>. - 14 + 2a + b = 0

==>. b = - 2a + 14 --------> equation 1

Similarly ,

(x + 1 ) is divisible

Let, x + 1 = 0

$\boxed{ x = - 1 }$

Substitute this value in place of x

we get ;

p(-1) = (-1) - 4 (-1)^2 + a (-1) + b

==>. - 1 - 4 (1) - a + b = 0

==>. - 1 - 4 - a - 2a + 14 = 0 ( substitute the value of " b " from equation 1 )

==>. - 5 - 3a + 14 = 0

==>. 9 - 3a = 0

==>. - 3a = - 9

Negative signs get cancelled on both sides

==>. 3a = 9

==>. a = 9/3

==>. a = 3

Value of b is

-2(3) + 14

= - 6 + 14

= 8

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