How do I find the roots of 3x^2-7x+5

Question

jhannybean · Answer

Have you learned the completing the square method?

dtan5457 · Answer

Yep. Looks like your either gonna complete the square or use the quadratic formula, your polynomial can't evenly be factored

mathstudent55 · Answer

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

jhannybean · Answer

@impossibledreams ?

anonymous · Answer

yes I have
@Jhannybean

jhannybean · Answer

okay :) So first group your x terms together.$$(3x^2-7x)+5$$Now factor out a 3.$$3\left(x^2-\frac{7}{3}x\right)+5$$Now complete the quadratic inside the parenthesis. $$3\left(x^2-\frac{7}{3}x+\frac{49}{36}\right)+5-\frac{49}{12}$$Simplify. $$3\left(x-\frac{7}{6}\right)^2 -\frac{11}{12}$$To find the roots,set it equal to 0.$$3\left(x-\frac{7}{6}\right)^2 = \frac{11}{12}$$Isolate your function by dividing both sides by 3.$$\left(x-\frac{7}{6}\right)^2 =\frac{11}{36}$$square root both sides. $$x-\frac{7}{6} = \pm \frac{\sqrt{11}}{6}$$Solve for x.$$x=\frac{7 \pm \sqrt{11}}{6}$$

dtan5457 · Answer

Oh my^

dtan5457 · Answer

Quadratic formula looks easier in this case, lol.

jhannybean · Answer

I showed every step of the process, some of these steps are mental math where the function is easily simplified :)