q8

Asked by nilesh.dhote74 | 22nd Apr, 2020, 09:48: PM

Expert Answer:

Q: Find the value of k in the following polynomials when
(i) (x+3) is a factor of (5x+4)3 - (3x+k)3
(ii) (x-2) is a factor of (3x+7)3 - (4x+k)3
Solution:
(i)
Let P(x) = (5x+4)3 - (3x+k)3
(x+3) is a factor of P(x)
Using converse of factor theorem, we can say that P(-3)=0
P(-3)=[5(-3)+4]3 - [3(-3)+k]3
Therefore, [5(-3)+4]3 - [3(-3)+k]3 = 0
[-15+4]3 - [-9+k]3 = 0
(-11)3 - (-9+k)3 = 0
(-9+k)3 = 113
-9+k = 11
k = 20
 
(ii)
Let Q(x)=(3x+7)3 - (4x+k)3
(x-2) is a factor of Q(x)
Using converse of factor theorem, we can say that Q(2)=0
Q(2)=[3(2)+7]3 - [4(2)+k]3
[3(2)+7]3 - [4(2)+k]3 = 0
[6+7]3 - [8+k]3 = 0
(13)3 - (8+k)3 = 0
(8+k)3 = 133
8+k = 13
k = 5

Answered by Renu Varma | 23rd Apr, 2020, 10:49: AM