The Student Room Group

Cubic equation conditions

The following curve is defined by the equation y=x36ax2+a2 \displaystyle y=x^3 -6ax^2+a^2 , where a a is a real number.
Given that the curve has 3 distinct real roots, find the range of values that a a can take.
Original post by Ano123
The following curve is defined by the equation y=x36ax2+a2 \displaystyle y=x^3 -6ax^2+a^2 , where a a is a real number.
Given that the curve has 3 distinct real roots, find the range of values that a a can take.


https://en.wikipedia.org/wiki/Cubic_function#The_discriminant
Original post by Ano123
The following curve is defined by the equation y=x36ax2+a2 \displaystyle y=x^3 -6ax^2+a^2 , where a a is a real number.
Given that the curve has 3 distinct real roots, find the range of values that a a can take.


Draw some examples of a graph of a cubic which has 3 distinct real roots. What do you notice about the turning points?
Original post by Ano123
The following curve is defined by the equation y=x36ax2+a2 \displaystyle y=x^3 -6ax^2+a^2 , where a a is a real number.
Given that the curve has 3 distinct real roots, find the range of values that a a can take.


Look @TeeEm 's Hard paper N
Reply 4
You really need to start including some of your own thoughts and attempts to your questions before posting them on TSR.
Reply 5
Original post by Zacken
You really need to start including some of your own thoughts and attempts to your questions before posting them on TSR.


A threat? Aimed at me?? :K::K:
I don't need to do anything.
(edited 7 years ago)
Reply 6
Original post by Ano123
A threat? Aimed at me?? :K::K:


No, not a threat... not sure where you got that from.
Reply 7
Original post by Zacken
No, not a threat... not sure where you got that from.


The pm you sent me saying, and I quote 'you will do me in'.
Reply 8
Original post by Ano123
The pm you sent me saying, and I quote 'you will do me in'.


lol you're off your rocker mate
Original post by Ano123
The pm you sent me saying, and I quote 'you will do me in'.


wht he means is ur on his turf and u been chattin maths shizzle so he wants to fight u.

Quick Reply

Latest