Question

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Answer 1

Question :-

The polynomials kx³ + 3x² - 3 and 2x³ - 5x + k leaves same remainder when divided by ( x - 4 ) . Find the value of k ?

Answer :-

Given :-

p ( x ) = kx³ + 3x² - 3

q ( x ) = 2x³ - 5x + k

( x - 4 ) when divided leaves same remainder

Required to find :-

• The value of k

Solution :-

p ( x ) = kx³ + 3x² - 3

( x - 4 ) when divides p ( x ) leaves remainder

So,

Let,

x - 4 = 0

x = 4

p ( 4 ) = k ( 4 )³ + 3 ( 4 )² - 3

= k ( 64 ) + 3 ( 16 ) - 3

= 64k + 48 - 3

= 64k + 45

However,

q ( x ) when divided by the ( x - 4 ) leaves remainder

Similarly,

It is mentioned that the remainder is equal in the both cases

So,

Let, x - 4 = 0

=> x = 4

q ( x ) = 2x³ - 5x + k

q ( 4 ) =

2 ( 4 )³ - 5 ( 4 ) + k = 64k + 45

2 ( 64 ) - 20 + k = 64k + 45

128 - 20 + k = 64k + 45

108 + k = 64k + 45

k - 64k = 45 - 108

- 63k = - 63

negative signs get cancelled

63k = 63

=> k = 63/63

=> k = 1

$\huge{\dagger{\boxed{\rm{ Value \; of \; k = 1 }}}}{\bigstar}$