57 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.Can someone help fast as i have a test at 2 o clock
can you send a clear pic?
suggestion:
put name of chapter, put name of concept in the post header :D you are going to find it hard to locate this doubt a few months down the line otherwise
Its the previous test
Phones arent allowed in the test
insta ban if that happens
:D
☠️
work backwards?
I did it by checking the options but i want another method for an approach
why though
test taking me you gotta find the quickest way to solve the q :D this should be it
Maths?
learning is diff from test taking.
But new approaches would help expand my knowledge base and so i can get better at solving problems
agar test 2 baje hai then abhi dont try and learn something new. just chill out. (of course people will help you with the proper solution etc)
not 4 hours before a test :P
Alr sir
okay, lets do this step by step from what is given in the question,
f (1) = 1
f (-1) = 5
this is clear?
if you take a general cubic expression
f(x) = ax^3 + bx^2 + cx + d
substitute in the above thingy,
a + b + c + d = 1
-a +b - c + d = 5
f(1)=1 right?
can you take it from here and make an attempt?
yup coefficient of x^2 + constant term = 3
yea typo :)
yes!
Going first principle route
add em up, b+d=3, the thing i said to check with coefficients....
so we have 4 variables, and 2 equations
how do you generate more equations?
differentiate :)
f'(x) = 3ax2 + 2bx + c
since you have (x-1)^2 and (x+1)^2 as factors, they will be factors of f'(x) too.
so you get two more equations
@Deleted User please solve from here.
Ok lemme try
I didnt understand this part
fixed the formatting. does it make sense now?
Ima just give this up for later after the exam, im just too dumb
like ax^2 + bx + c for a quadratic equation, for a cubic you have one more term, that is it
as (x-1) is a factor of {f(x) - 1};
when you put x = 1 in the function, f (1) -1 = 0
Ohhh
f(1) =1 and f(-1)=5
similarly, as (x+1) is a factor of {f (x)-5}:
when x = -1, f (-1) - 5 = 0
it is cancer to write math like this in chat. ngl
I got this part
i see why comrade uses latex now xD
cool
Why do the coefficients add up to 1 ?
Oh coz x's become 1 coz we need the whole thing to become 0
But why would it how can we say that its one if it has to be divisible by (x+1)² which is 4 ?
Then wont f(1) have to be 5 ?
right
@iTeachChem
divisible by x + 1 means that the root is -1
hence it was written as f (-1) -5 = 0
So divisible means the numerator has to become zero ?
which then becomes f (-1) = 5 :)
exactly. that is the root of the equation :) (it is a factor right)
check out this topic on Khan Academy
explains the basics well
Dont the factors dividing their multiples give one ?
when you factorise somehting simple as x^2 −3x+2 You write it as (x-3)(x-2)
this means that at x = 3 and x = 2, the function becomes 0 (crosses the x axis i.e.)
why would that be?
So the root of (x+1)² would have to be in the numerator as to be divisible i understand now
Khan Academy
Finding zeros of polynomials (1 of 2) (video) | Khan Academy
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
watch this
yea that is a repeated root, if f(x) and f'(x) will both have the same root
differentiation abhi padha hai kya? My b shouldve asked this :D
Basic part padha hai physics ke lie
haan utna kafi hai
and my suggestion for the future, watch KA videos jab bhi koi concept ki foundation banani ho
Ok sir
chal ab go chill ho gaya ye sort :P
relax before a test, sabse zaroori ye hai :) all the best
Ek min b+d = 3 aagya to me options check krlunga right
Ok ty sir 🙏
ji. wahi thanos ne bola tha shuru me
Ooh ab samaj aaya
b+d=3 a+c = -2 to kisi me nai aara kya kru 😦
you sure?
Nope
aaram se kar
koi jaldi nahi :)
Oh shit im dumb option 2 right?
-3 ko b samaj rha tha
gj!
Finally ty sir and thanos bhaiya
+solved @iTeachChem @Deleted User
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