polynomials (1 Viewer)

[enigma_1]

Find the turning points of the polynomial 4x^3 − x^4 − 1 and hence state how many zeroes
they have.

How do you find how many zeroes they have?
Answer: 2 zeroes

 

[QZP]

I believe the question is asking for the zeroes of the gradient function, otherwise the 'hence' part is throwing me off :S

 

[HeroicPandas]

So find the stationary points of the polynomial and their nature, then draw up a quick inaccurate graph and there should be 2 x-intercepts

 

[enigma_1]

nah, I'm pretty sure it aint. Cause for this example, 3x^4 − 4x^3 + 2,

The answer is zero...wtff

 

[enigma_1]

Heroic pandas! How do I draw it..

 

[HeroicPandas]

Heroic pandas! How do I draw it..

let polynomial be y

I got (0,-1) being a point of inflection and (3,26) being a maximum

As x--> -infinity, y --> - infinity
As x--> infinity, y--> -infinty

It looks like a mountain

 

[QZP]

Heroic pandas! How do I draw it..

There is a turning point at x = 3. Find F(3) and the value on the immediate left/right to establish the concavity at that point. Then you should be able to determine how many zeroes there are It's just translating the information from the graph of your gradient function (though there are many other ways to conceptualise it). HeroicPandas is right.

 

[hit patel]

It is possibly asking you for double roots or asking you to find the concavity at the point by y'' and y' and therefore drawing a sketch to obtain possible number of roots. Believe it or not but that is 4U maths from somwhere in the second / first exercise hyperbole .

 

[enigma_1]

Ohh, thanks hit, Heroic pandas, QZP!

Ahaha really? Well that justifies my freak out lol!

 

[Vision]

Ohh, thanks hit, Heroic pandas, QZP!

Ahaha really? Well that justifies my freak out lol!

Sorry to say, but sketching the graph isn't 4u, you should be learning it in 3u. You'll probably learn it soon though.

 

[hit patel]

Sorry to say, but sketching the graph isn't 4u, you should be learning it in 3u. You'll probably learn it soon though.

Terry lee 4 U Text Book Exercise 3.1 Q5).

 

[Carrotsticks]

It is possibly asking you for double roots or asking you to find the concavity at the point by y'' and y' and therefore drawing a sketch to obtain possible number of roots. Believe it or not but that is 4U maths from somwhere in the second / first exercise hyperbole .

The curve is a polynomial, and sketching polynomials (even with the aid of calculus) is in 3U.

Hell, even basic polynomial sketching is in 2U, but they are not identified as polynomials.