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show how the quadratic formula can be used to rewrite : f(x) = 9x^2 - 149x - 234IN FACTORED FORM

Show How The Quadratic Formula Can Be Used To Rewrite Fx 9x2 149x 234IN FACTORED FORM class=

Sagot :

To factor the function using the quadratic formula we equate it to zero and solve for x:

[tex]\begin{gathered} 9x^2-149x-234=0 \\ x=\frac{-(-149)\pm\sqrt[]{(-149)^2-4(9)(-234)}}{2(9)} \\ x=\frac{149\pm\sqrt[]{30625}}{18} \\ x=\frac{149\pm175}{18} \\ \text{then} \\ x=\frac{149+175}{18}=18 \\ or \\ x=\frac{149-175}{18}=-\frac{26}{18}=-\frac{13}{9} \end{gathered}[/tex]

Now we write the function as:

[tex]f(x)=(x-a)(x-b)[/tex]

where a and b are the roots we found above, then we have:

[tex]\begin{gathered} f(x)=(x-18)(x-(-\frac{13}{9})) \\ f(x)=(x-18)(9x+13) \end{gathered}[/tex]

Therefore:

[tex]f(x)=(x-18)(9x+13)[/tex]