Cubic Equation 2 | CAT Preparation 2024 | Algebra | Quantitative Aptitude
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- Опубликовано: 14 окт 2024
- Advance Algebra by Ravi Prakash | Quantitative Aptitude for CAT 2024
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At 15:40 : 2ac is 2*1*25
Sir , what is this 2ac , i think it should be 4ac na ??, please reply..🙏
@SARTHAK BORA 🤡
@SARTHAK BORA 🤡
@@sachinkumarsingh2518 it's a condition ig. Not a discriminate
@@mindfullmallu7511 correct
Where is descartes sign rule video?
RESPECTED SIR
KINDLY CLARIFY ONE DOUBT
IN X^3+5X^2+25X+125
2AC SHOULD BE 2*1*25 AND NOT 2*1*125.KINDLY CLEAR THE DOUBT.
WITH REGARDS
ROHIT SHARMA
Your perception is correct sir made a little mistake their
nigga wrote a whole ass application lmao
why did we use b^2 - 4ac previously and now its b^2 - 2ac? What's the difference between the two?
It's a condition...not a discriminant
Great Job sir. You are a real Hero! Thanks a Million times!
Why is the Discriminant of the cubic equation (b^2-2ac) and not (b^2-4ac)? Please help.
Because that's not the DISCRIMINANT, it's just a condition.
There's nothing like b^2-2ac like quadratic equation,in cubic equation we have to compare b^2 to 2ac , if it is less then 2 imaginary roots and 1 real root.
Else all roots are real.
You are using 125 instead of 25. So please pine a comment for confirmation..
Yes isn't that a mistake ? Like c is supposed to be 25 i guess he used the value of d ..
At 4:55 answer will be 13/4
We are given that , , and are the roots of the equation:
x^3 - 2x^2 + 3x - 2 = 0
We are tasked with finding .
Step 1: Use Vieta's formulas
For a cubic equation of the form , Vieta's formulas give us relationships between the coefficients and the roots:
P + q + r = 2, \quad Pq + qr + Pr = 3, \quad Pqr = 2
Step 2: Find the expression
We start by rewriting as:
\frac{1}{P^2} + \frac{1}{q^2} + \frac{1}{r^2} = \frac{q^2r^2 + P^2r^2 + P^2q^2}{P^2q^2r^2}
From Vieta's formulas, we know , so .
Now, we need to find . We can express this using the identity:
q^2r^2 + P^2r^2 + P^2q^2 = (Pq + qr + Pr)^2 - 2(P^2 + q^2 + r^2)
We already know , so:
(Pq + qr + Pr)^2 = 3^2 = 9
Now, we need to find . This can be computed using the identity:
P^2 + q^2 + r^2 = (P + q + r)^2 - 2(Pq + qr + Pr)
Substituting the known values:
P^2 + q^2 + r^2 = 2^2 - 2(3) = 4 - 6 = -2
Step 3: Final calculation
Now substitute back into the expression for :
q^2r^2 + P^2r^2 + P^2q^2 = 9 - 2(-2) = 9 + 4 = 13
Thus:
\frac{1}{P^2} + \frac{1}{q^2} + \frac{1}{r^2} = \frac{13}{4}
The final answer is 13/4
It's 1/4 only use chatgpt.
does cubic eqn have more vids or is it just the 2 vids?
Hi Sir, Thanks for the series. I wanted to know where is the "Descartes sign change rule" video ?
Did you find it?
@@MaxwellNaradd no
At 8:01 shouldn’t the equation 3 be equal to -b ?
Yesss
yes sir told it in a different way, like b is negative so value is negative only.
@@kanakh7775hi
Did you clear the cat?
@@lazy_ChattoreI did, yes! Didn’t do an MBA though.
@@kanakh7775 got call from IIMs?
How much did you score?
hey can anyone share the descartes sign change rule video link
Amazing concepts!!! Thank you sir❤️
If apna= beta= gamma= delta=3
Then this root must satisfy the equation of bi-quadratic mentioned here which is not!
Can anyone suggest me if I am wrong anywhere ?
I think you have done something wrong in the calculations
Answer of the eqn by putting x=1(let's say), its coming out to be equal to 16 instead of 0 & by putting X=2 , Eqn. equals to 1 , why so ????? Can anyone clarify this doubt ...
Wrong Calculation. It is satisfying. Putting x=3, eq=0
At 15:55 should c be eual to 25 instead of 125?
Yeah .. thanks for figuring it out.. we have recorded more than 300 videos, so even after reviewing there can be small errors in around 5% of the videos . I will again review and I will put an ERRATA comment for correction.
@@raviprakash6021 Please upload more videos. Less than 3 months for CAT 2019.
yes
@@raviprakash6021 thank s sir for all your efforts.
@@raviprakash6021 Thanks Sir for the effort and time you had put to make us understand the topic. :)
What is the use of calculating the value of one root among the three roots in the last question? How will that help to solve the question further?
Then you use that factor(E.g. if 1 is a root, (x-1) is a factor) and divide the whole cubic equation by this factor using long division method to get a quadratic equation. Then solve the quadratic to find the other 2 roots.
You can use synthetic division method to reduce the equation to quadratic and solve quadratic for other two roots.
Dear Sir,
Good Morning
At 8:40 , facing problems till the end of this question, because after putting the values in the equation, values doesn't satisfy the equation, please check once..
Nope..equation satisfies✅✅
b must be negative
at 11:50 if the roots are non negative then how come the b is -108
B is not a root
b is not a root it is a coeffiecient of x
Thanks for your efforts, Sir.
Wlcm😊
Why we can take abcd as the roots instead of alpha gama bita??
Abcd = 3*3*3*3
B= 3
A=3
At 15 condition is not satisfying for eqn x^3+2x^2-3x-10=0 ....which has one real root at x=2 and 2img roots
Sir in the first eqn the roots are p,q,r. Now at x=1 the equation satisfy. one of the roots is 1. whatever we add to 1 we'll get the answer as greater than 1, then how can the answer be 0.25
Ok so the question is wrong as 1 root is real and two are imaginary ✌️. Discriminant= -4
Thanku sir
anyone know the ans. of last equation? pls tell
Sir, where is the next video containing Descartes sign change rule as you have mentioned in the video. Kindly help
did you get it ?
Sir very nice conceptual video ❤️
Thank you so much sir
hi. Can anyone pls share the cubic equation part 3 link... The playlist has cubic equation part 3 but it has quadratic eqn lecture.
There is only 2 video of cubic eqn
Thankyou 💜 so much sir 🙏🏻
Thank you Sir🙏
At 14.17... The discriminant of cubic equation is b^2-3ac and not 2ac...
Well That's not at all a discriminant he is saying. That's just a condition.
At 11:13 now he has taken minus sign where as in last video he took positive sign😕😕😕
@@sapeduworld Here the condition is different.
Here we have four roots while in the last video we had 3 roots.
Actually u need to understand properly how those roots are being evaluated!!
Similarly when we will have 5 roots and 6 roots, it will be different.
Try to understand the pattern properly. So that u know what will be for n no. of roots!!
@@avinashnair8433 Bro plz tell from where i can get more info about how these roots work...plz send the link if any
@@sapeduworld Watch Ravi Sir's introduction video of Cubic Equation.
Sir explained those concepts really well 🙂
Discriminant is b^2 - 4ac na...
Yaar wahi toh yahan 4ac hona chaahiye na, bahut confuse ho gya iss video me...If you got proper explanation of this 2ac , please reply ..
@@sachinkumarsingh2518 bhai ye discriminant nahi hai ye bas ek condition hoti hai jo cubic equation pe apply hoti hai. Or wo jo b^2-4ac hota hai vo bas quadratic equation ke liye hota hai.
Thank you.
At 4:48 how can denominator be equal to 4???
Bcoz in question p²q²r² is given in denominator and the formula is pqs = -d/a means =2 so p²q²s² = 2² = 4. Hope u understand.
❤❤
thank u sir❤
I wanted to know where is the "Descartes sign change rule" video ? Can you please help ?
🙏🙏
I wanted to know where is the "Descartes sign change rule" video ? Can you please help ?
☑
Thank u sir🙏