Solving cubic with a value other than one (2 Viewers)

[shaon0]

wtf I thought china > russia

I think Russia>China

 

[Timothy.Siu]

they wont give u a stupid one for HSC

 

[Slidey]

australia is bad at maths in general

Actually, that's false. We're near the top of the OECD for maths education.

 

[Ostentatious]

I once heard my friend say you can find the roots of a cubic by inspection. Has anyone ever heard of this method and if so, how do you go about it?

 

[Timothy.Siu]

I once heard my friend say you can find the roots of a cubic by inspection. Has anyone ever heard of this method and if so, how do you go about it?

err self explanatory, u look at it and u find a root...how else can u do it by inspection

 

[Ostentatious]

How do you even go about it though? Are there little knacks that hint towards what they are? For example, in (monic) quadratics we learn that we group the expression into two terms with x's and the numbers that multiply to get c and add to get b. Are there similar methods in cubics?

PS, I haven't really done polynomial theory, if that is necessary.

 

[youngminii]

How do you even go about it though? Are there little knacks that hint towards what they are? For example, in (monic) quadratics we learn that we group the expression into two terms with x's and the numbers that multiply to get c and add to get b. Are there similar methods in cubics?

PS, I haven't really done polynomial theory, if that is necessary.

LOL are you talking about sum/product of roots?
In a quadratic, the sum of roots = -b/a, product of roots = c/a
You can't actually find the roots using this method though, unless additional info is given in the question (ie. the roots are the same, or consecutive etc)

@ OP. If you REALLY wanted to find the roots to that cubic (or at least an estimate), you could always draw a rough sketch (hell, you can even use calculus) and then use bisection/Newton's method to find the roots(or in this case, root). Won't take that long.

 

[buchanan]

say the equation given was 7x^3 − 5x^2 − 2x+24 = 0

By dividing the equation by 7 and then using the <a href="http://users.tpg.com.au/nanahcub/cubic.gif">cubic formula</a>, we find that the exact value of x is

[maths]\sqrt[3]{\frac{-15436}{9261}+\sqrt{\frac{59957}{21609}}}+\sqrt[3]{\frac{-15436}{9261}-\sqrt{\frac{59957}{21609}}}+\frac{5}{21}[/maths]

 

[gurmies]

I'm Russian, and I think that China >= Russia...either way, both have great mathematicians.

 

[Templar]

In terms of secondary education in maths China is superior to Russia. It also depends on what you mean by everything exactly. We might be near the top of OECD by some statistics but it doesn't mean we aren't a bunch of idiots compared with some countries.

 

[youngminii]

By dividing the equation by 7 and then using the cubic formula, we find that the exact value of x is

[maths]\sqrt[3]{\frac{-15436}{9261}+\sqrt{\frac{59957}{21609}}}+\sqrt[3]{\frac{-15436}{9261}-\sqrt{\frac{59957}{21609}}}+\frac{5}{21}[/maths]

Cubic formula, ey?