Answer:
[tex]y=6x^2-5x+1[/tex]
Step-by-step explanation:
If the quadratic equation has a root at [tex]\dfrac13[/tex] then when [tex]x=\dfrac13[/tex], [tex]y=0[/tex]
[tex]\implies x=\dfrac13[/tex]
[tex]\implies 3x=1[/tex]
[tex]\implies 3x-1=0[/tex]
If the quadratic equation has a root at [tex]\dfrac12[/tex] then when [tex]x=\dfrac12[/tex], [tex]y=0[/tex]
[tex]\implies x=\dfrac12[/tex]
[tex]\implies 2x=1[/tex]
[tex]\implies 2x-1=0[/tex]
Therefore, [tex]y=(3x-1)(2x-1)[/tex]
[tex]\implies y=6x^2-5x+1[/tex]
