11please dont get angry
check my pst#11[1]
What is the no of real roots in 2\left|x^3 \right| + 3x^2 -12\left|x \right| + 1 = 0 ?
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24 Answers
11ques is an even function
so symettric about both the quadants[1]
1arey none of them will be used...
btw, i got 4 real roots.. sum1 confirm....
11k sir will not say anything like this again
but rolle therom and lagrange mean value theorems r to be banked upon na
62mani.. dude it makes a lot of sense.. seriously...
Please dont ignore such questions...
11if x>0 then it becomes
2x3+3x2-12x+1=0
its roots r x=1.75....,0.085,-3.34 straight 4m Microsoft math
SO THERE R 2 SOLUTIONS 4 IT
if x <0 then eq becomes
-2x3+3x2+12x+1=0
its roots r -0.085,-1.75,3.34 straight 4m Microsoft math
SO ITS ROOTS R ALSO 2
TOTAL NUMBER OF ROOTS OF THIS EQUATION IS 4
BUT DO REMEMBER ME THAT DO NOT WASTE TIME ON THESE TYPE OF PROBLEMS AS SOLUTION OF CUBIC EQUATION IS NOT IN THE SYLLABUS OF IIT JEE
1MANIPAL THIS IS TOO MUCH IN THE SYLLABUS !!
TAKE DERIVATIVE...
FIND MAX-MIN ...
CHCEK THE FUNCTION VALUE AT THOSE POINTS...
DRAW THE GRAPH...
SEE AT HOW MANY POINTS IT CUTS THE X-AXIS...
DONE..
11this is a pretty useful info but it will lead to a round about value and not to the exact value
the above post is very essential as rolle theorem is asked in IIT JJEE in variety of forms
but sir this ques in IIT JEE makes no sense
its graph could be made but this will become a long and a lenghty 1 [2]
21f(a).f(b) bein -ve implies there exists 'c' such dat f(c) == 0 as the function is continous over (a,b)
Intermediate value therm jaisa hi kuch
62The roots will lie between a maxima and minima
This information sometimes helps a lot in solving such problems.
How do you use this information..
f(a) x f(b) <0
why think a bit more
11SIR I DONT KNOW HOW TO FIND THE 1ST ROOT OF A CUBIC EQUATION
I ALWAYS USE HIT AND TRIAL
PLAESE HELP ME OUT IN THESE TYPE OF PROBLEMS[1]
24yup sir is right.........................ignoring everything will put us into trouble becoz JEE is bound to bring surprises to students
62Manipal..
something that are not in syllabus but one should know them
I strongly thing that this is one of them.
Please dont ignore these...
11SORRY TO REPEAT MYSELF AGAIN
CUBIC FUNCTIONS R NOT IN JEE
4 MORE INFO
http://www.winentrance.com/engineering_entrance_exam/iit_jee/IIT-JEE-Syllabus.html
1but i won't have something like that when i write an exam,this was actually in a comprehension of calculus qns,which involved finding the above function,i repeat what do i do if i get such a qn in an exam,can't use any software there