Question

Find the value of ‘K’ if on the division of p(x)= 2x^3-3x^2-7x+k by x – 2, the remainder is 2.

Answer 1

Given :-

p ( x ) = 2x³ - 3x² - 7x + k is divided by ( x - 2 ) leaves remainder 2

Required to find :-

• Value of ' k '

Method used :-

>> Remainder theorem <<

Solution :-

Given information :-

p ( x ) = 2x³ - 3x² - 7x + k is divided by ( x - 2 ) leaves remainder 2

we need to find the value of ' a '

Consider ;

p ( x ) = 2x³ - 3x² - 7x + k

when ( x - 2 ) divides p ( x ) it leaves remainder 2

So,

Let ;

=> x - 2 = 0

=> x = 2

Substitute , the value of x in p ( x )

p ( 2 ) =

2 ( 2 )³ - 3 ( 2 )² - 7 ( 2 ) + k = 2

Here, we need to equal the whole polynomial to zero because when ( x - 2 ) divides p ( x ) it leaves remainder 2

So,

2 ( 8 ) - 3 ( 4 ) - 14 + k = 2

16 - 12 - 14 + k = 2

Transpose 2 to the left side

16 - 12 - 14 - 2 + k = 0

16 - 28 + k = 0

- 12 + k = 0

This implies,

=> k = 12

Therefore,

Value of " k " is 12

Verification :-

Here, we need to verify whether our answer is correct or not .

So,

Substitute the value of the k in the polynomial

p ( x ) = 2x³ - 3x² - 7x + k

=> p ( x ) = 2x³ - 3x² - 7x + 12

Now,

Let's divide the polynomial with ( x - 2 ) and verify whether the remainder is 2 or not by using remainder theorem .

p ( 2 ) =

2 ( 2 )³ - 3 ( 2 )² - 7 ( 2 ) + 12 = 2

2 ( 8 ) - 3 ( 4 ) - 14 + 12 = 2

16 - 12 - 14 + 12 = 2

( - 12 , + 12 gets cancelled )

16 - 14 = 2

2 = 2

LHS = RHS

Hence verified !

Answer 2

Answer:

YOUR QUESTION :

Find the value of ‘K’ if on the division of p(x)= 2x^3-3x^2-7x+k by x – 2, the remainder is 2.

SOLUTION :

As divisor is x-2, u hv to put 2 in the polynomial,

$2*2^3-3*2^2-7*2+k=2 \\ = > 16-12-14+k=2 \\ = > K=2+10=12</p><p></p><p>$