# P(x^2)+x*q(x^3)+x^2*r(x^3)=(1+x+x^2)*s(x), p(1)=ks(1) and r(1)=kp(1). Then k=?????

##### 1 Answer

Jul 9, 2018

See below

#### Explanation:

From

we get

Given

This equation can be solved easily for

*However, I can't help feeling that there was one more relation in the problem which got missed out somehow. For, example, if we had one more relation like #q(1) = kr(1)#, we would have had #{q(1)}/{s(1)} = k^3#, and the final equation would have become*

#k^3+k^2+k-3 = 0 implies#

#k^3-k^2+2k^2-2k+3k-3=0implies#

#(k-1)(k^2+2k+3)=0#

Now, since #k^2+2k+3=(k+1)^2+2 ge 2#, it can not vanish for real #k#. So we must have #k=1#