Q9 of 90 Page 2

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

x3 – 6x2 + 11x – 6;3

Given zeroes is 3


So, (x – 3) is the factor of x3 – 6x2 + 11x – 6


Let us divide x3 – 6x2 + 11x – 6 by x – 3


The division process is



Here, quotient = x2 – 3x + 2


= x2 – 2x – x + 2


= x(x – 2) – 1(x – 2)


= (x – 1)(x – 2)


So, the zeroes are 1 and 2


Hence, all the zeroes of the given polynomial are 1, 2 and 3.


More from this chapter

All 90 →
7

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

t2 – 5t + 6,t2 + 11t – 6

 8

Give examples of polynomials p(x), g(x), q(x) and r(x) satisfying the Division Algorithm

p(x) = g(x).q(x) + r(x),deg r(x)<deg g(x)


And also satisfying


(i) deg p(x) = deg q(x) + 1


(ii)deg q(x) = 1


(iii) deg q(x) = deg r(x) + 1

 9

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

x4 – 8x3 + 23x2 – 28x + 12;1,2

 9

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

x3 + 2x2 – 2; – 2