What are the zeros of the function #f(x)= 3x^2-3x-6#?

2 Answers
Feb 9, 2017

Answer:

#x=-1# and #x=2#

Explanation:

Step 1. Factor out the function you were given

#f(x)=3x^2-3x-6#
#" "=3(x^2-x-2)# ...factor out #3#, common to all three terms
#" "=3(x+1)(x-2)# ...identify a factorization of the polynomial

Step 2. Set the factored function equal to zero and solve

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

  • #3# is not zero
  • #(x+1)=0# when #x=-1#
  • #(x-2)=0# when #x=2#

Step 3. Verify these roots are zeros of the function by graphing

Socratic.org graph, modified by MS Paint

Feb 9, 2017

Answer:

#x=-1,x=2#

Explanation:

The zeros of f(x) are the values of x which make f(x) = 0

#"solve "3x^2-3x-6=0#

#rArr3(x^2-x-2)=0larr" common factor of 3"#

#rArr3(x-2)(x+1)=0larr" factorise quadratic"#

#x-2=0rArrx=2larr" is a zero"#

#x+1=0rArrx=-1larr" is a zero"#