Question

Obtain all zeroes of the polynomial 2x4 + x3 – 14x2 – 19x – 6,if two of its zeroes are -2 and -1

Answer 1

ANSWER

All zeroes are = -2, -1, -1/2, 3

EXPLANATION

GIVEN

two zeroes are = -2 and -1

x = -2 and x = -1

x + 2 and x + 1

SOLUTION

products of zeroes

(x + 2) ( x + 1 )

x^2 + 3x + 2

divide this equation of polynomial

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

on dividing we get,

2x^2 - 5x - 3

split this quotient into middle term split

2x^2 - 5x - 3 = 0

2x^2 - 6x + x - 3 = 0

2x ( x - 3 ) +1 ( x - 3 ) = 0

(2x + 1 ) ( x - 3 ) = 0

x = -1/2 and x = 3

Hence, all zeroes are

-2, -1, -1/2, 3