Q. 25.0( 1 Vote )

Find the number o

Answer :

Given, p(x) = x3 + 1


To find the zeros of p(x), consider p(x) = 0


x3 + 1 = 0


(x + 1) (x2 – x + 1) = 0 Using the identity (a + b)3 = (a + b) (a2 – ab + b2)


x + 1 = 0 or x2 – x + 1 = 0


x = –1 ; real zeros of x2 – x + 1 are not possible.


–1 is the only zero of p(x).


Since –1 is real, number of real zeros is 1.


The given polynomial has degree 3, so it can have 3 zeros at most.


No. of zeros = 3 ; No. of real zeros = 1


For p(x) = x3 + 1, taking x = –2, –1, 0 and 2.


We obtain the following table:



Plotting these points on graph paper, we obtain the following figure:



It can be seen that the graph intersects the X-axis at (–1, 0), so –1 is the zero of p(x).


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 :

Find the number oGujarat Board Mathematics

Draw the graph ofGujarat Board Mathematics

Find the number oGujarat Board Mathematics