Quadratic with fractions - completing the square or formula

Doing past papers at the mo & have a quadratic which I am stuck on

find fixed points of f(x) = x^2+(13/12)x-1/2

Now, fixed points are when f(x) = x, so I have subtracted x from both sides

=> x^2 + (1/12)x - 1/2 = 0 to make an easier(?) quadratic

so a=1, b=1/12 & c=-1/2

Sub into formula & I am now stuck as the sqrt comes up as negative & I'm not sure enough about completing the square.

I also have similar equation f(x) = x^2 + (14/15)x - 2/5. Stuck here, too (Speechless)

Would appreciate a little help.

Thank you

Re: Quadratic with fractions - completing the square or formula

$\displaystyle x^2+\Big( {1 \over 12}\Big)x-\frac{1}{2}=0$

$\displaystyle D=\Big( {1 \over 12}\Big)^2-4\Big( -\frac{1}{2}\Big)=\frac{1}{144}+2=\frac{289}{144} \quad(\text{... which is positive})$

You can also multiply both sides by 12 to get

$\displaystyle 12x^2+x-6=0$

$\displaystyle \implies x= \frac{-1 \pm \sqrt{1-4(-6)(12)}}{12(2)}$

Re: Quadratic with fractions - completing the square or formula

Hi.

I have the second example, too, which I have still not been able to do. Similar equation f(x) = x^2 + (14/15)x - 2/5

Please could someone point me in the right direction with this, too. It is part of a fixed point iteration question.

I'm having trouble with that, too, but I must keep trying.

Re: Quadratic with fractions - completing the square or formula

Quote:

Originally Posted by

**froodles01** Doing past papers at the mo & have a quadratic which I am stuck on

find fixed points of f(x) = x^2+(13/12)x-1/2

Now, fixed points are when f(x) = x, so I have subtracted x from both sides

=> x^2 + (1/12)x - 1/2 = 0 to make an easier(?) quadratic

so a=1, b=1/12 & c=-1/2

Sub into formula & I am now stuck as the sqrt comes up as negative & I'm not sure enough about completing the square.

I also have similar equation f(x) = x^2 + (14/15)x - 2/5. Stuck here, too (Speechless)

Would appreciate a little help.

Thank you

Are you trying to find the x intercepts for the second? If so...

$\displaystyle \displaystyle \begin{align*} x^2 + \frac{14}{15}x - \frac{2}{5} &= 0 \\ x^2 + \frac{14}{15} + \left(\frac{7}{15}\right)^2 - \left(\frac{7}{15}\right)^2 - \frac{2}{5} &= 0 \\ \left(x + \frac{7}{15}\right)^2 - \frac{49}{225} - \frac{90}{225} &= 0 \\ \left(x + \frac{7}{15}\right)^2 - \frac{139}{225} &= 0 \\ \left(x + \frac{7}{15}\right)^2 &= \frac{139}{225} \\ x + \frac{7}{15} &= \pm \frac{\sqrt{139}}{15} \\ x &= \frac{-7 \pm \sqrt{139}}{15} \end{align*}$

Re: Quadratic with fractions - completing the square or formula

Oooh! (Surprised) Ideal. This DOES make my understanding better (as well as having the answer). I'll get there one day.