Find the value of k if the expression x3 + kx2 +3x - 4 leaves a remainder of -2 when divided by x + 2.
Answers
Answer :-
k = 4
Solution :-
Let f(x) = x³ + kx² + 3x - 4
If x³ + kx² + 3x - 4 is divided by x + 2 4 leaves remainder - 2
Finding zero of x + 2
⇒ x + 2 = 0
⇒ x = - 2
By Remainder theorem
Remainder = f(-2)
Given,
Remainder = - 2
⇒ f(-2) = 2
⇒ ( - 2 )³ + k( - 2 )² + 3( - 2 ) - 4 = - 2
⇒ - 8 + k( 4 ) - 6 - 4 = - 2
⇒ - 8 + 4k - 10 = - 2
⇒ 4k - 18 = - 2
⇒ 4k = - 2 + 18
⇒ 4k = 16
⇒ k = 16/4 = 4
Therefore the value of k is 4.
QUESTION :-
Find the value of k if the expression x3 + kx2 +3x - 4 leaves a remainder of -2 when divided by x + 2.
SOLUTION :-
==> let, f(x) = x³+ kx2 +3x - 4
==> .°. find zero of x +2.
==> x +2=0
==> x = -2 .
==> .°. Remainder = f(-2) [ by applying Remainder theorem]
==> Given : Remainder = -2
==> .°. f(-2) = 2.
==> f(-2)= (-2)³ + k(-2)² +3(-2) -4
==> -8 + 4k -6-4 = -2
==> -8 +4k -10 = -2
==> 4k - 18 = -2
==> 4k = 16
==>.°. k = 4