rational zeros f(x)=x^3+10x^2+14x-6

Question

f(x)=x^3+10x^2+14x-6 Use the Rational Zero Therom to list all the possible rational zeros.

Answer 1

f(x) = x^3+10x^2+14x-6

By the rational root therom

Since the leading cooefficient is 1 and constant term is -6.

So the possible rational zeros are ±1,±2,±3,±6.

Now test the each of the possibilities.

P(1) = (1)^3+10(1)^2+14(1)-6 = 1+10+14-6 = 19

P(-1) = (-1)^3+10(-1)^2+14(-1)-6 = -1+10-14-6 =  -12

P(2) = (2)^3+10(2)^2+14(2)-6 = 8+40+28-6 = 70

P(-2) = (-2)^3+10(-2)^2+14(-2)-6 = -8+40+28-6 = 54

P(3) = (3)^3+10(3)^2+14(3)-6 = 27+90+42-6 = 153

P(-3) = (-3)^3+10(-3)^2+14(-3)-6 = -27+90-42-6 = 15

P(6) = (6)^3+10(6)^2+14(6)-6 = 216+360+84-6 = 654

P(-6) = (-6)^3+10(-6)^2+14(-6)-6 = -216+360-84-6 = 54