# Obtain all zeros of polynomial 2x^4+x^3-14x^2-19x-6, if two of its zeroes are -2 & -1. Pls and soon!

1
by sanjays2402

2015-04-22T15:33:51+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
P(x) = 2 x⁴ + x³ - 14 x² - 19 x - 6
The number of sign changes in the coefficients : of P(x) = 1
the number of sign changes in the coefficients of  P(-x) = 3

There are atmost 3 negative real roots and 1 positive real root.

two roots or zeros are :  -2 and -1.
So (x+2) and (x+1) are the factors of  P(x).

P(x) = (x² + 3 x + 2) (a x² + b x + c) = 2 x⁴ + x³ - 14 x² - 19 x - 6

comparing both sides we can say that:
a = 2     and  c = - 3.
the coefficient of  x³ on both sides are :    3 a + b = 1
b = -5

The roots of :  2 x² - 5 x - 3  = 0
(2 x + 1 ) ( x - 3 ) = 0
x = - 1/2    or  3