Finding Roots & Zeros for polynomial equations

[sherlockkirby]

My question is this: if I put the polynomial in the graphing calculator and can't quite see where the graph crosses the X axis (no matter how close I zoom), and it looks as if it runs along the X axis for awhile, dips below, and then goes up, then how can I tell how many real zeros it has? Since it is the general U-shape, it seems like it has 2 real zeros and 2 imaginary, but the graph is just weird. Any ideas how to more clearly read it? I need to find the number of real and imaginary zeros for a problem like this: 3x⁴ + 2x³

Thanks so much!!

Sherlock

 

[pka]

Well for \(\displaystyle 3x^4+2x^3=0 \) there are just two roots: \(\displaystyle 0,~\frac{-2}{3}. \)

 

[mmm4444bot]

Any ideas how to more clearly read [the graph]?

Reduce the vertical range in the window settings. What calculator are you using?

 

[Deleted member 4993]

My question is this: if I put the polynomial in the graphing calculator and can't quite see where the graph crosses the X axis (no matter how close I zoom), and it looks as if it runs along the X axis for awhile, dips below, and then goes up, then how can I tell how many real zeros it has? Since it is the general U-shape, it seems like it has 2 real zeros and 2 imaginary, but the graph is just weird. Any ideas how to more clearly read it? I need to find the number of real and imaginary zeros for a problem like this: 3x⁴ + 2x³

Thanks so much!!

Sherlock

3x⁴ + 2x³ = 3x³ * (x + 2/3)

As you can the roots of this equation are at x = 0 and x = - 2/3. At x=0, the function has repeating roots, thus you have the curve "flattened" there.