Question

obtain all other zeroes of the polynomial f(x)=2x4+x3-14x2-19x-6,if its two zeroes are -2 and -1.

Answer 1

zeroes are -2,-1,-1/2,3....

Answer 2

Answer:

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

Step-by-step explanation:

Given Expression:

$2x^4+x^3-14x^2-19x-6$

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,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-3)}}{2(2)}=\frac{5\pm\sqrt{25+24}}{4}$

$x=\frac{5\pm7}{4}$

$x=\frac{5+7}{4}=3\:\:and\:\:x=\frac{5-7}{4}=\frac{-1}{2}$

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