Question

Obtain all the zeros of the polynomial 3x^4 + 6x^3 – 2x^2 – 10x – 5, if two of its zeros are root 5/3 and – root 5/3

Answer 1

Hello,

Please refer the above photograph for the used process.

By factor theorem we got the factors of p(x)
Now,

Assume a number that is 12
2 and 3 are factors of 12
Also 3*2 that is 6 is a factor of p (x)

Similarly,
If
$(x + \sqrt{ \frac{5}{3} }) \: and \: (x - \sqrt{ \frac{5}{3} } )$
Are the factors of p(x)
Then,
$(x + \sqrt{ \frac{5}{3} } )(x - \sqrt{ \frac{5}{3} } )$
Is also a factor of p (x)

Hence we got that x²-5/3 is a factor of p(x) using identity (a+b) (a-b) = a²-b²

Hope this will be helping you ✌️

Answer 2

Answer:

Step-by-step explanation: