Question

Obtain all zeros of (3x4 − 15x3 + 13x2 + 25x − 30), if two of its zeros are √5/3 and -√5/3. Please answer in text ( no pictures please)

Answer 1

Answer:

Obtain all the zeros of 3x4+6x3−2x2−10x−5, if two of its zeros areroot 35​

​ androot −35​

​

Step-by-step explanation:

f(x)=3x4+6x2−2x2−10x−5

Given, 35​

​ and −35​

​ are the zeros of f(x).

∴⎝⎜⎛​x−35​

​⎠⎟⎞​(x+35​

​) are the factors of f(x).

(x2−35​

​) are the factor of f(x) or (3x2−5) are the factor of f(x).

So, 3x4+6x3−2x2−10x−5

=(3x2−5)(x2+2x+1)

=3(x2−35​)(x+1)2

=3⎝⎜⎛​x−35​

​⎠⎟⎞​⎝⎜⎛​x+35​

​⎠⎟⎞​(x+1)2

∴ Zeros are 35​

​,−35​

​,−1 and −1.