Question

Find the zeroes of polynomial x cube - 2x square - x + 2​

Answer 1

TO FIND

Zeros of the following polynomials ,

$p(x) = {x}^{3} - 2 {x}^{2} - x + 2$

SOLUTION

By Remainder Theorem we have tried factors of 2 like 1, -1 , 2 , -2 etc.

Finally we got 1 as a zero of p(x)

p(1) = 1^3 - 2 × 1^2 -1 + 2

=> 1 - 2 - 1 + 2 = 0

By factor theorem ,

x - 1 is a factor of p(x)

We will now divide p(x) By x - 1by long division method ( In the attachment File)

Hence we got that p(x) can be written as

(x - 1)(x^2 - x - 2)

=>( x - 1)(x^2 -2x + x -2)

=> (x - 1)[x(x - 2) + 1 (x - 2)]

=> (x - 1)(x + 1)(x - 2)

Hence the factors (zeros) of p(x) are

x - 1 = 0

=> x = 1

x + 1 = 0

=> x = -1

x - 2 = 0

=> x = 2

Hence the zeros of the polynomial are -1 ,1 and 2.

Answer 2

Answer:

hence , Zeroes are

-1,2 ,1.

hope it helpsss....