Tips on complicated quadratic factoring?

Question

Hi all,

Factoring (t^2)+4t-672=0 was required for a OG question. Any tips on how to approach this other than trial and error using the answer choices?

BrushMyQuant · Answer

How about using the quadratic formula? https://en.wikipedia.org/wiki/Quadratic_formula

RR88 · Answer

I usually use prime factorisation while dealing with big numbers such as 672 here. You can really quickly multiply prime factors to create possible factors adhering to sum of roots a.k.a. b.

For e.g. 672 = 2*2*2*2*2*3*7 = 2*2*2*3*2*2*7 = 24*28.

But then it all comes down to individual preference and comfort for a particular method.

Sent from my MotoG3-TE using  GMAT Club Forum mobile app

Cez005 · Answer

Thanks, that's not a bad suggestion but it can still be long-winded to find the root. Any tips on finding the root of a large number like 2704?

Would you just narrow down the range of possible numbers. E.g. 50^2 is 2500 and 60^2 is 3600, so the sqrt must be between 50 and 60. The only integers that. when squared, result in a units digit of 4, are 2 and 8. Trying 52^2 gives the answer.

BrushMyQuant · Answer

I prefer long division https://www.math-only-math.com/square-ro ... ethod.html Sent from my Redmi Note 4 using GMAT Club Forum mobile app

Bunuel · Answer

Solving and Factoring Quadratics: https://www.purplemath.com/modules/solvquad.htm https://www.purplemath.com/modules/factquad.htm Hope it helps.

ganand · Answer

Hi  Cez005 ,

There are mainly three ways to solve the quadratic equation problems.
1. Using formula
2. Middle term factorization method, and
3. Method of completing Square

I'll explain the Method of completing Square.

Any quadratic equation of the form  ax^{2} + bx + c = 0  can be transformed into  a(x+d)^{2} + e = 0 ,
where  d = \frac{b}{2a} 	extrm{ and } e = c - \frac{b^{2}}{2a}

In the given example, we have  a = 1, b = 4 	extrm{ and }c = -672 
 d = 4/2 = 2, e = -672 - 16/4 = -676

Hence, we have  (t + 2)^{2} - 676 = 0 \Rightarrow (t+2)^{2} = 26^{2} \Rightarrow t+2 = \pm 26 \Rightarrow t = 24 	extrm{ or } -28

For more detail please visit  completing-square.html

Please remember squares of 1 to 30.  what-to-memorize-in-gmat-quant-for-the-gmat .

Hope this helps.

Tips on complicated quadratic factoring?

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