Question

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

Answer 1

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

`\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=(149\pm175)/(18) \\ \text{then} \\ x=(149+175)/(18)=18 \\ or \\ x=(149-175)/(18)=-(26)/(18)=-(13)/(9) \end{gathered}`

Now we write the function as:

`f(x)=(x-a)(x-b)`

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

`\begin{gathered} f(x)=(x-18)(x-(-(13)/(9))) \\ f(x)=(x-18)(9x+13) \end{gathered}`

Therefore:

`f(x)=(x-18)(9x+13)`