I am revising for a lifwynnfoundation.orgematics exam and also am looking over simultaneous equations. I was curious as to as soon as I use the quadratic formula and also when I don"t? I realize there are multiple means to fix a question - for example 2x^2+7x-15=0 - deserve to I use the simultaneous equation for this or do I just use the factorizing method?



I always attempt to use the factorizing method initially. But periodically the technique does not job-related for specific quadratic equations. In that situation, I resort to making use of the quadratic formula$$x=frac-b pm sqrtb^2-4ac2a$$For your equation of $2x^2+7x-15=0$, we have actually $a=2,b=7,c=-15$.

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


*

If you have the right to factorize your quadratic without making use of the formula then you must carry out it, because it is normally faster.

When you have actually a quadratic $ax^2+bx+c$ you can easily factorize it if you deserve to discover 2 numbers $n_1,n_2$ such that $n_1+n_2=b$ and also $n_1n_2=ac$ by recomposing $bx$ as $n_1x+n_2x$ and then grouping comparable terms.

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

$2x^2+7x-15=0$$2x^2+10x-3x-15=0$$2x(x+5)-3(x+5)=0$$(2x-3)(x+5)=0$


*

Key Idea $ $ Use AC-technique to minimize to factoring a polynomial that"s $, mcolor#c00monic,$ (lead coeff $=color#c001)$

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


*

*

It"s my see that the quadratic formula should always be used to variable a quadratic. That"s what it"s for.

Completing the square must be used to transform a quadratic into vertex-emphasis develop (and to derive the quadratic formula).

Factoring by grouping is just really taught at the HS level to offer students an introduction to Number Theory (finding integer options to equations, analyzing factors and residuals, etc), or probably as a preliminary for developing strategies for factoring cubics. Other than that, it"s not extremely advantageous.


Thanks for contributing an answer to lifwynnfoundation.orgematics Stack Exchange!

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

But avoid

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up via recommendations or personal suffer.

Use lifwynnfoundation.orgJax to format equations. lifwynnfoundation.orgJax recommendation.

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

To learn more, view our tips on creating excellent answers.


Blog post Your Answer Discard

By clicking “Article Your Answer”, you agree to our terms of business, privacy plan and also cookie policy


Not the answer you're looking for? Browse various other questions tagged quadratics or ask your very own question.


site design / logo design © 2021 Stack Exreadjust Inc; user contributions licensed under cc by-sa. rev2021.9.17.40233


Your privacy

By clicking “Accept all cookies”, you agree Stack Exreadjust deserve to keep cookies on your gadget and also disclose information in accordance through our Cookie Policy.