ns am revising because that a lifwynnfoundation.orgematics exam and also am looking end simultaneous equations. Ns was curious as to when I usage the quadratic formula and also when i don"t? ns realize there are multiple means to deal with a question - for example 2x^2+7x-15=0 - can I usage the coincided equation for this or perform I simply use the factorizing method?

I always shot to use the factorizing an approach first. However sometimes the an approach does not work-related for specific quadratic equations. In that case, I will to utilizing the quadratic formula$$x=\frac-b \pm \sqrtb^2-4ac2a$$For her equation that $2x^2+7x-15=0$, we have $a=2,b=7,c=-15$.

You are watching: How to know when to use the quadratic formula


If you can factorize your quadratic without making use of the formula then you need to do it, since it is normally faster.

When you have actually a quadratic $ax^2+bx+c$ you can easily factorize that if you can discover two number $n_1,n_2$ such that $n_1+n_2=b$ and $n_1n_2=ac$ through rewriting $bx$ as $n_1x+n_2x$ and also then grouping similar terms.

In the case of $2x^2+7x-15=0$ we have actually $n_1=10$ and also $n_2=-3$ so us factorize the without having to usage the quadratic formula:



Key Idea $\ $ use AC-method to mitigate to factoring a polynomial that"s $\,\rm\color#c00monic\,$ (lead coeff $=\color#c001)$

$$\quad\ \ \begineqnarrayf &\,=\,& \ \ 2\ x^2+\ 7\ x\ -\,\ 15\\\Rightarrow\ 2f &\,=\,&\ (2x)^2\! +7(2x)-30\\ &\,=\,& \ \ \ \color#c00X^2+\,7\ X\ -\,\ 30,\,\ \ X\, =\, 2x\\ &\,=\,& \ \ \,(X-3)\ (X+\,10)\\ &\,=\,& \ \ (2x-3)\,(2x+10)\\\Rightarrow\ f\,=\, 2^-1(2f) &\,=\,& \ \ (2x - 3)\,(x+5)\\\endeqnarray\qquad\qquad$$



It"s my view that the quadratic formula should always be offered to factor a quadratic. That"s what it"s for.

Completing the square must be used to change a quadratic into vertex-focus form (and to derive the quadratic formula).

Factoring by group is only really teach at the HS level to provide students an development to Number theory (finding integer remedies to equations, evaluating factors and residuals, etc), or possibly as a preliminary for emerging strategies for factoring cubics. Other than that, it"s not very useful.

Thanks for contributing response to lifwynnfoundation.orgematics stack Exchange!

Please be sure to answer the question. Provide details and also share your research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; earlier them up with referrals or personal experience.

Use lifwynnfoundation.orgJax to format equations. Lifwynnfoundation.orgJax reference.

See more: Us State Nicknamed The Pine Tree State, Maine State Nickname

To learn more, view our tips on writing an excellent answers.

short article Your prize Discard

By click “Post her Answer”, friend agree to our terms of service, privacy policy and cookie plan

Not the prize you're spring for? Browse other questions tagged quadratics or questioning your own question.

site style / logo © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.9.17.40233

her privacy

By click “Accept all cookies”, girlfriend agree ridge Exchange can store cookie on your an equipment and disclose information in accordance with our Cookie Policy.