Question

Determine the value of k if P(x) = kx3 + 4x2 +3x - 4 and q(x) = x3 - 4x + k leaves the same remainder when divided by ( x - 3 )

Answer 1

Answer :-

k = - 1

Solution :-

p(x) = kx³ + 4x² + 3x - 4

q(x) = x³ - 4x + k

When p(x) and q(x) are divided by (x - 3) leaves same remainder

Finding zero of x - 3

==> x - 3 = 0

==> x = 3

By remainder theorem

• When p(x) divided by (x - 3), p(3) is remainder
• When q(x) divided by (x - 3), q(3) is remainder

Given

Remainder when p(x) divided by (x - 3) = Remainder when q(x) divided by (x - 3)

==> p(3) = q(3)

==> k( 3 )³ + 4( 3 )² + 3( 3 ) - 4 = ( 3 )³ - 4( 3 ) + k

==> k( 27 ) + 4( 9 ) + 9 - 4 = 27 - 12 + k

==> 27k + 36 + 9 - 4 = 15 + k

==> 27k + 45 - 4 = 15 + k

==> 27k + 41 = 15 + k

==> 27k - k = 15 - 41

==> 26k = - 26

==> k = - 26/26 = - 1

Therefore the value of k is - 1.

Answer 2

Answer:

Step-by-step explanation:

Given :-

p(x) = kx³ + 4x² + 3x - 4

q(x) = x³ - 4x + k

To Find :-

Value of  k.

Solution :-

When p(x) and q(x) are divided by (x - 3) gives x - 3

=  x - 3

= x = 3

Using Remainder Theorem,

Remainder when p(x) divided by (x - 3) = Remainder when q(x) divided by (x - 3)

⇒ p(3) = q(3)

⇒ k( 3 )³ + 4( 3 )² + 3( 3 ) - 4 = ( 3 )³ - 4( 3 ) + k

⇒ k( 27 ) + 4( 9 ) + 9 - 4 = 27 - 12 + k

⇒ 27k + 36 + 9 - 4 = 15 + k

⇒ 27k + 45 - 4 = 15 + k

⇒ 27k + 41 = 15 + k

⇒ 27k - k = 15 - 41

⇒ 26k = - 26

⇒ k = - 26/26

⇒ k = - 1

Hence, the value of k is - 1.