Find all the zeros of the polynomial 
, if two of its zeros are 2 and −2.
Answers
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) = x⁴ + x³ - 34x² -4x +120
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 - 4
[(a+b)(a - b) = a² - b² ]
x² - 4 is a factor of given Polynomial f(x)
Now, Divide f(x) =x⁴ + x³ - 34x² -4x +120 by g(x) = x² - 4
[DIVISION IS IN THE ATTACHMENT.]
Hence , all the zeroes of the given Polynomial are: (2), (- 2), -6 & 5
HOPE THIS ANSWER WILL HELP YOU …..
Answer:
roots=a,b
product of roots=120
ab×−4=120
ab=−30
a=−
b
30
a+b+2−2=−1
b−
b
30
=−1
b
2
+b−30=0
b
2
+6b−5b−30=0
b(b+6)(b−5)=0
roots are=5,−6