Question

conjugate factor theorem.. does it apply for real roots? if 3+0i is a root 3-0i also a root ??

Answer 1

but a polynomial only has n roots?? what if degree 2.. 3+0i and 3-0i both root how can u have the other or 3+0i and 3-0i count as one

Answer 2

that is ur misconception if u find the root
say (x-3)^2 it is having mathematically two roots 3,3

Answer 3

whut .. thats caue multiciplity =2
okay take x^2+4x+3=0 (x-3)(x-1)=0 x=3,1

Answer 4

no u have not taken my point in depth
see if u shift this parabola y=(x-3)^2 by 1 unit down u get two roots
but if it was having single root then it will never be the case
that matters a lot!!

Answer 5

huh o-o
yeah so for my example.. youre saying that the roots would be x=3,3,1,1 because they have to occur in conjugagtes ?

Answer 6

no it is not the case in ur second reply but it was indeed in first reply
because there conjugate was hidden in the quadratic formula(in ur second reply)

Answer 7

what do u mean hidden ??

Answer 8

i mean when we write quadratic formula for
ax^2 +bx +c=0
then (-b(+/-)(b^2-4ac)^1/2)/2a the term in square root is the conjugate term

Answer 9

it can have conjugate by taking for one time + and another time -

Answer 10

r u getting it or not

Answer 11

in short, conjugate theorem does not apply to real roots, if 3+0i is factor, u cannot say 3-0i is also the factor......what else is the confusion?

Answer 12

no hartnn mathematically they are two different roots with same MAGNITUDE

Answer 13

nopes, they are same roots.....i mean 3+0i=3-0i=3 and u cannot consider magnitude or angle as both are real numbers not complex at all.

Answer 14

the magnitude of a real number does not quite make sense
if defined,its value is same a that of the number.

Answer 15

i do not believe
if shift the graph of y=(x-3)^2 one unit down then it has two roots which can not be the case if it has only distinct roots
any such graphical trans formation can not change the number of roots

Answer 16

if u shift the graph of y=(x-3)^2 one unit down then
the new equation will be y-1=(x-3)^2
as all the points now have their new y co-ordinate as y-1
\((x-3)^2=0\) had two equal solutions 3,3 -?grapg cutting at only x=3
\((x-3)^2+1=0\) will have 2 distinct solutions
which implies graph cuts at 2 distinct points............

Answer 17

when u are shifting the graph,the equation of graph changes and so does the intercepts , got it @RajshikharGupta ?

Answer 18

alright thanks hartnn :)

Answer 19

isnt equation y=(x-3)^2-1 if u shift down ?

Answer 20

oh yes, thanks for pointing it out
Y=y-1 so
y=Y+1
so new equation:
Y+1=(X-3)^2
or
Y=(X-3)^2+1

Answer 21

sorry Y=(X-3)^2-1

Answer 22

i m not satisfied with ur explanation
out of my intuitions!!!

Answer 23

so just plot it and see...
y=(x-3)^2
and y=(x-3)^2-1

Answer 24

same graph different roots

Answer 25

ofcourse same graph will have different roots(roots= x intercepts)
depending on where u place the graph.......