Determine which of the given numbers are roots of the polynomial f(x)= 6x^2+x-1

Question

esa_pau · Answer

a. 1/2, 1
b.-1/2,2 
c. -1/2
d. 1
i know its not B

vuriffy · Answer

Just plug them in and try.

vuriffy · Answer

6x^2+x-1 = 0
Let's try -1/2
6(-1/2)^2-1.5 = 0 
6(1/4) - 1.5 = 0
1.5 - 1.5 = 0. 
That means it is a solution.

vuriffy · Answer

-1/2 - 1 = - 1.5, by the way.

vuriffy · Answer

0 = 0.

esa_pau · Answer

alright got it thanks

vuriffy · Answer

Sweet, great job.

sshayer · Answer

$$6x^2+3x-2x-1=3x(2x+1)-1(2x+1)=(2x+1)(3x-1)$$
2x+1=0
x=-1/2
3x-1=0
3x=1
x=1/3
from here you can see your option.

esa_pau · Answer

u lost me

vuriffy · Answer

The polynomial had two solutions, but your question only gave one of them, which is why I only demonstrated one, whereas @sshayer did both.

esa_pau · Answer

ahh so it  just gave me half an answer in the multiple choice?

vuriffy · Answer

Technically, yes, it did. But, you only need the one which had -1/2, so it was okay.