What are all the possible rational zeros for #f(x)=3x^2+2x-1#?

1 Answer
Mar 18, 2017

Answer:

Zeros are #1/3# and #-1#

Explanation:

Observe that in quadratic function #f(x)=3x^2+2x-1#, the discriminant #b^2-4ac=2^2-4xx3xx(-1)=16# is a perfect square and hence, we can factorize it with rational factors,

#f(x)=3x^2+2x-1#

= #3x^2+3x-x-1#

= #3x(x+1)-1(x+1)#

= #(3x-1)(x+1)#

Hence, zeros are given by #3x-1=0# and #x+1=0#

i.e. they are #1/3# and #-1#