solve quadratic equation and tell some easy method to do it

Question

anonymous · Answer

$$3x ^{2} + 15x + 9 = 0 $$

hartnn · Answer

i would recommend the formula

hartnn · Answer

Compare your quadratic equation with $ax^2+bx+c=0$
find a,b,c
then the two roots of x are:
 $\huge{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$

anonymous · Answer

yes, that's easiest way i know

anonymous · Answer

can't we go for middle term spilt?

hartnn · Answer

check b^2-4ac, if it is perfect square, then we can split the middle term

anonymous · Answer

b^2 - 4ac = 15^2 -4*3*9
=225-108
=117
is it right?

anonymous · Answer

yes 117 is not a perfect square

hartnn · Answer

so we can't split

parthkohli · Answer

I always recommend the formula, though factoring works if you need speed.

anonymous · Answer

what is significance of this sign?
$$\pm $$

hartnn · Answer

that there are 2 roots, one considering + sign and other considering - sign

anonymous · Answer

ok thanx
so there is no simple way to this type of quadratic equation bcoz i don't like calculations?

hartnn · Answer

you can use completing square method , then, but i won't say its easier....

anonymous · Answer

what is that method?

hartnn · Answer

3x^2+ 15x+ 9= 0
first make the co-efficient of x^2 as 1
divide the equation by 3, what u get ?

anonymous · Answer

x^2 + 5x +3 = 0

hartnn · Answer

now take the co-efficient of x, divide it by 2 and square it, what u get ?

anonymous · Answer

25/4 x

hartnn · Answer

just 25/4 , not x 
so add and subtract 25/4 in that equation

anonymous · Answer

ok
x^2 + 5x + 3 + 25/4 - 25/4 = 0

hartnn · Answer

right , 
now write it like this : 
(x^2 + 5x + 25/4 )+ (3- 25/4) = 0
where (x^2...) is a perfect square

anonymous · Answer

what about
3 - 25/4 ??

hartnn · Answer

transfer that to other side 
(x^2 + 5x + 25/4 ) = 25/4-3

hartnn · Answer

so u get (x+...)^2=..
take sqrt on both sides

anonymous · Answer

so it become 
(x + 5/2)^2 = 13/4
sqrt of both sides
x + 5/2 = sqrt ( 13/4)

hartnn · Answer

when u take sqrt, u get 2 values, + or -
x + 5/2 = $\pm$sqrt ( 13/4)

anonymous · Answer

ok now i understood it
well thanx
so can i close it now?

hartnn · Answer

yes, if u understand the steps and can do other similar problems, u can..

anonymous · Answer

well thanx

hartnn · Answer

welcome ^_^