x2 - 45x + 324 = 0
middle term splitting method?

Question

x2 - 45x + 324 = 0 
middle term splitting method?

ajprincess · Answer

Can u find two numbers a and b such that
a+b=-45
a*b=324?

unklerhaukus · Answer

$$324=2\times162=2^2\times81=2^2\times3^4$$

anonymous · Answer

also can you tell me the technique to split high value integers

anonymous · Answer

@UnkleRhaukus  it is only factorization of 324. how will it help to split the terms??

anonymous · Answer

@ajprincess  i can find the p(x) with product and sum of roots

unklerhaukus · Answer

$$2\times2\times3\times3=36$$
$$3\times3=9$$

anonymous · Answer

thank you i understand now..:)

unklerhaukus · Answer

$$x^2 - 45x + 324 = 0 $$
$$\left(x^2-(36+9)x+(36\times9)\right)=0$$

anonymous · Answer

thank you everybody for helping me and also for taking a look too :)
bye!!

directrix · Answer

@Ekaansh The technique is known as "busting the b," the name coming from the b coefficient of the linear x term in the expression ax^2 +bx + c where a is not 0. Follow this link to several examples of busting the b: http://mysite.cherokee.k12.ga.us/personal/randy_smith/site/Lists/Math%203%20Class%20Notes/Attachments/78/Alg%20Rev%20C%20Day%203%20notes.pdf

unklerhaukus · Answer

if the numbers are nice enough and small enough ,  this technique can be done in ones head.,    In all other cases i would just use the quadratic formula because i can always remember it and it always works , (even for complex solutions) ,

But If you trying the 'busting the b' method, it is a good idea to factorise the large numbers