GIVEN
[tex] \\ [/tex]
Roots: x= 1/2 & x= 3/4
[tex] \\ \\ [/tex]
Transfer the denominators to the left side. Multiply the denominators to x.
[tex] \\ 2x = 1 \: \: and \: \: 3x = 4 \\ \\ [/tex]
Transfer the constant to the left side. Change their integer signs
[tex] \\ 2x - 1 = 0 \: \: and \: \: 3x - 4 = 0 \\ \\ [/tex]
Multiply 2x-1 to 3x-4. Use F.O.I.L. Method
[tex] \\ (2x - 1)(3x - 4) \\ \\ 6 {x}^{2} - 8x - 3x + 4 = 0 \\ \\ [/tex]
Add all same terms
[tex] \\ 6 {x}^{2} - 11x + 4 = 0 \\ \\ [/tex]
Change the equation to quadratic function.
[tex] \\ \green{\boxed{ \bold{y = 6 {x}^{2} - 11x + 4} }} \: \: or \: \: \\ \green{\boxed{ \bold{f(x) = 6 {x - 11x + 4}^{2} }} }\\ \\ \\ [/tex]
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