Question

Obtain all zeros of the polynomial $f(x)= 2x^{4} +x^{3}-14x^{2}-19x-6$ if two of its zeros are -2 and -1.

Answer 1

Method of finding the remaining zeros of a polynomial when some of its zeros are given:

We firstly write the factor of polynomial using given zeros and multiply them to get g(x). Then divide a given polynomial by g(x).

The quotient so obtained give other zeros of given polynomial and we factorise it to get other zeros.

SOLUTION:

Let f(x) = 2x⁴  +x³  –14x²  - 19x  - 6

Given : Two Zeroes of the polynomial are - 2 & -1. Therefore ,    

(x + 2) & (x +1) are the two factors of given Polynomial f(x).

(x + 2) (x +1)  = x² + 1x + 2x + 2  

= x² + 3x + 2

x² + 3x + 2 is a factor of given Polynomial f(x)

Now, Divide f(x) = 2x⁴  + x³  –14x²  - 19x  - 6 by g(x) = x² + 3x + 2.  

[DIVISION IS IN THE ATTACHMENT.]

Hence , all the zeroes of the given Polynomial are: (- 2), (-1), 3 ,-1/2

HOPE THIS ANSWER WILL HELP YOU …..

Answer 2

Answer:

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