Finding the Irrational roots of this Equation

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-Whiplash-

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Jan 22, 2014
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Hi, I was given the following question and I've been working on it for hours and I have no idea how to solve it due to it having no Rational roots.

Find all possible roots to the nearest tenth for:

6x3+6x2+15x-2=0

Can I get some advice on where to even start? I tried Synthetic Division, long division and factoring but nothing works due to this problem having no Rational roots, it's driving me nuts.
 
-Whiplash- said:
Hi, I was given the following question and I've been working on it for hours and I have no idea how to solve it due to it having no Rational roots.

Find all possible roots to the nearest tenth for:

6x3+6x2+15x-2=0

Can I get some advice on where to even start? I tried Synthetic Division, long division and factoring but nothing works due to this problem having no Rational roots, it's driving me nuts.
Click to expand...

The only way I know to estimate real irrational roots of cubics or higher involves numerical analysis. What method/s have you been taught?
 
Denis said:
Not to "scare you away!", but if you enter your equation in an online-equation-solver,
you'll get these 3 beauties as solution:

solution 1
x = -13*(sqrt(3)*i/2-1/2)/(18*(5*sqrt(35)/36+59/108)^(1/3))+(5*sqrt(35)/36+59/108)^(1/3)*(-sqrt(3)*i/2-1/2)-1/3

solution 2
x = (5*sqrt(35)/36+59/108)^(1/3)*(sqrt(3)*i/2-1/2)-13*(-sqrt(3)*i/2-1/2)/(18*(5*sqrt(35)/36+59/108)^(1/3))-1/3

solution 3
x = (5*sqrt(35)/36+59/108)^(1/3)-13/(18*(5*sqrt(35)/36+59/108)^(1/3))-1/3

In case you didn't know: i means SQRT(-1)

Just pray to the spirit of Isaac Newton that you don't get a similar one on a timed test :rolleyes:
Click to expand...

.... Show off..... :grin::grin::grin:
 
Subhotosh Khan said:
The only way I know to estimate real irrational roots of cubics or higher involves numerical analysis. What method/s have you been taught?
Click to expand...

I told you what methods I was taught, none of them work.

I actually know the answers already because I used a graphing calculator, but I have to show your work full points, but whatever then, it's only one question
 
-Whiplash- said:
I told you what methods I was taught, none of them work.

I actually know the answers already because I used a graphing calculator, but I have to show your work full points, but whatever then, it's only one question
Click to expand...
None of the methods you've been taught could work, because they don't apply. So I suspect that there is a typo in the exercise. ;)
 
I got estimates by zooming in on the x-interept (accurate to four places). I called this root R.

I divided the cubic polynomial by x-R, to get a quadratic polynomial with coefficients in decimal form.

The quadratic formula gave me the two Complex roots (and I rounded those the nearest tenth).
 
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