SOLUTION: if x=-2/3 and x=1/4 are the roots of the quadratic equation ax^2+bx+c=0,then which of the following could represent the two factors of ax^2+bx+c? F. (3X+2)and (4x-1) G. (3X+1)

Algebra ->  Equations -> SOLUTION: if x=-2/3 and x=1/4 are the roots of the quadratic equation ax^2+bx+c=0,then which of the following could represent the two factors of ax^2+bx+c? F. (3X+2)and (4x-1) G. (3X+1)       Log On


   

Question 633749: if x=-2/3 and x=1/4 are the roots of the quadratic equation ax^2+bx+c=0,then which of the following could represent the two factors of ax^2+bx+c?
F. (3X+2)and (4x-1)
G. (3X+1) and (4X-2)
H. (3X-1) and (4x+2)
J. (3x-2) and (4x+1)
K. (3x-2) and (4x-1)
Would it be good to substitute each of -2/3 and 1/4 for x? like this below
3(-2/3)+2 4(1/4)-1
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

if x=-2/3 and x=1/4 are the roots of the quadratic equation ax^2+bx+c=0,

then which of the following could represent the two factors of ax^2+bx+c? 

 (3x+2)(4x-1) = 0   | yes one could do the substituting of the roots.

Many will recognize from factoring and finding solutions, in general...that

IF 

 (3x+2)(4x-1) = 0 

THEN

  x = -2/3   and x = 1/4

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
it would be good to substitute each of -2%2F3 and 1%2F4 for x and see if each factor is equal to zero:
recall that the quadratic equation ax%5E2%2Bbx%2Bc=0 represent the two factors %28x+%2B+m%29%28x+%2B+n%29=0
now, check your options:
F. %283x%2B2%29and %284x-1%29..it would be
%283x%2B2%29%284x-1%29=0
now, check each factor:
%283x%2B2%29=0......substitute -2%2F3 for x
%283%28-2%2F3%29%2B2%29=0
%28cross%283%29%28-2%2Fcross%283%29%29%2B2%29=0
-2%2B2=0
0=0
check the second factor
%284x-1%29=0......now substitute 1%2F4 for x
%284%281%2F4%29-1%29=0
%28cross%284%29%281%2Fcross%284%29%29-1%29=0
1-1=0
0=0.....as you can see both factors are equal to zero, and this is your solution
so, you can check the other options and you will see they are not solutions