Question

Find all the zeroes of the polynomial p(x) =2x3+3x2-11x-6 if one of its zero is -3

Answer 1

Answer:

x=2,-1/2 and -3

Step-by-step explanation:

Given, p(x) = 2x^3+3x^2-11x-6

if, -3 is a zero then (x+3) is a solution of it. Then,

2x^3+3x^2-11x-6=0

or, 2x^3+6x^2-3x^2-9x-2x-6 = 0

or, 2x^3(x+3)-3x(x+3)-2(x+3) = 0

or, (x+3) (2x^2-3x-2) = 0

Then,

x= -3

and,

2x^2-3x-2=0

or, 2x^2-4x+x-2 = 0

or, 2x(x-2) +1(x-2) = 0

or, (x-2) (2x+1) = 0

So,

x = 2 and x = -1/2

So the all zeros are,

x = -3,2 and -1/2