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)   (Show Source): You can put this solution on YOUR website!
 it would be good to substitute each of  and  for  and see if each factor is equal to zero:



recall that the quadratic equation  represent the two factors 



now, check your options:



F. and ..it would be







now, check each factor:



......substitute  for 



















check the second factor



......now substitute  for 















.....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





 

RELATED QUESTIONS

If the roots of a quadratic equation are -4 and 1, write the equation in... (answered by solver91311)

If the roots of the quadratic equation ax*2+bx+c=0 are in the ratio of 2 : 3,
then prove  (answered by greenestamps)

if the roots of a quadratic equation are -3 and 3, write the equation in ax^2+bx+c=0... (answered by stanbon,ewatrrr,Alan3354)

if the equation x^4+ax^2+bx+c=0 has roots 1,2,and 3 Find... (answered by richard1234)

If both the roots of the quadratic equatin ax^2+bx+c=0 are infinite,then a=b=0 and 
c... (answered by ikleyn)

If the equation x^4+ax^2+bx+c=0 has roots 1,2,3 Find... (answered by stanbon)

if the roots of a quadratic equation are (-2+sqrt 6) and (-2-sqrt 6), what is the... (answered by solver91311,fcabanski,Onmyoji.S)

Al-khwarizmi solved all quadratic equations by reducing them to one of six standard... (answered by CPhill)

How do I write a quadratic equation with the given roots (2/3) and -4  in the form of... (answered by ankor@dixie-net.com)