Question

find all the zero of the polynomial 3 x ^4 - 15 x ^3 + 17 x ^2 + 5 x - 6 if two of its zeros are 1 /√3 and -1/√3.
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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

hey there!

you can solve this question by the method used in this question as well

Step-by-step explanation:

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) = x³  + 3x²  - 2x - 6

Given : Two Zeroes of the polynomial f(x) are - √2 & √2. Therefore , (x + √2) & (x - √2) are the two factors of given Polynomial f(x).

(x + √2) (x - √2)   = x² - (√2)²

= x² - 2

[(a+b)(a - b) = a² - b² ]

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

Now, Divide f(x) = x³  + 3x²  - 2x - 6 by g(x) = x² - 2

[DIVISION IS IN THE ATTACHMENT.]

Hence , all the zeroes of the given Polynomial are: (√2), (- √2), -3 .

HOPE THIS ANSWER WILL HELP YOU …..