Question

obtain all zeros of the polynomial f(x)=2x4+x3-14x2-19x-6 , if two of its zeros are - root 3 and root 3​

Answer 1

Answer:

All zeroes of the given polynomial are -2 , -1 , 3 and -1/2.

Step-by-step explanation:

Given Expression:

Zeroes of given expression are -2 & -1.

We need to find all zeroes.

From Given Zeroes, we have following factors ( x + 2 ) and ( x + 1 )

⇒ x² + 3x + 2

Now We divide given polynomial by x² + 3x + 2

to get another quadratic polynomial.

After division we get,

Quotient = 2x² - 5x - 3

Now we find zeroes of obtained quadratic polynomial ot find last 2 zeroes of given polynomial.

using Quadratic formula,

Therefore, All zeroes of the given polynomial are -2 , -1 , 3 and -1/2.