Answer :

Given, ax3 + bx2 + cx + d


Need to show a = – c and b = – d if x2 – 1 is a factor


consider, x2 – 1 is a factor of ax3 + bx2 + cx + d


then x = + 1, x = – 1


substitute x value in the equation ax3 + bx2 + cx + d


We get as follows


for x = 1 we get a(1)3 + b(1)2 + c(1) + d


= a + b + c + d ……..eq(1)


for x = – 1 we get a(– 1)3 + b(– 1)2 + c(– 1) + d


= – a + b – c + d ………eq(2)


Solving the two equations we get


(a + b + c + d) + (– a + b – c + d) = 0


b + d = 0


b = – d


And if (a + b + c + d) – (– a + b – c + d) = 0


a + c = 0


a = – c


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

What first degreeKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2