Finding the zeroes for cubic equation

  • Thread starter dmoney123
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In summary: Either way, good job on finding the correct solutions!In summary, the conversation is about finding the zeroes for the function f(x)=x^3+25x. The attempt at a solution involved factoring the equation to get the zeroes as 0, -5i, and 5i. The person then checked their solutions using substitution and found that they all worked. However, the solution given to them was incorrect, causing frustration and self-doubt. The summary concludes with praise for finding the correct solutions.
  • #1
dmoney123
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1

Homework Statement



Find all zeroes for the function f(x)

f(x)=x^3+25x

Homework Equations


The Attempt at a Solution



I tried factoring out x out of it.

x(x^2+25)

and again to give

x[(x+5i)(x-5i)]

this would give me the 0,-5i,+5i as the zeroes. Doesn't seem to be right though.

Any thoughts?

Thanks!
 
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  • #2
dmoney123 said:

Homework Statement



Find all zeroes for the function f(x)

f(x)=x^3+25x


Homework Equations





The Attempt at a Solution



I tried factoring out x out of it.

x(x^2+25)

and again to give

x[(x+5i)(x-5i)]

this would give me the 0,-5i,+5i has the zeroes. Doesn't seem to be right though.

Any thoughts?

Thanks!

Try substituting in your three solutions, to see if they work. You should always check your solutions this way, and you can certainly do it as easily as we can.
 
  • #3
(5i)^3+25(5i)=
-125i+125i=0

(-5i)^3+25(-5i)=
125i-125i=0

0^3+25(0)=0

seems to check out for me. however this is not giving me the correct answer according to the solution
 
  • #4
dmoney123 said:
(5i)^3+25(5i)=
-125i+125i=0

(-5i)^3+25(-5i)=
125i-125i=0

0^3+25(0)=0

seems to check out for me. however this is not giving me the correct answer according to the solution

Your solution is correct, so that must mean that the solution you were given is wrong.
 
  • #5
Thanks for your help. Sure is frustrating when you start doubting yourself. Take care.
 
  • #6
You could also have checked the incorrect solutions you were given for peace of mind.
 

1. How do you find the zeroes for a cubic equation?

To find the zeroes for a cubic equation, you can use the cubic formula or the Rational Root Theorem. The cubic formula involves plugging in the coefficients of the equation into a formula, while the Rational Root Theorem involves factoring the equation and testing possible rational roots.

2. What is the cubic formula?

The cubic formula is a mathematical formula used to find the zeroes of a cubic equation. It is also known as the Cardano formula and involves plugging in the coefficients of the cubic equation into a formula to find the three possible solutions.

3. Is there a faster way to find the zeroes of a cubic equation?

Yes, the Rational Root Theorem is often a faster method to find the zeroes of a cubic equation. It involves factoring the equation and then testing possible rational roots to find the actual zeroes.

4. Can a cubic equation have more than three zeroes?

No, a cubic equation can only have a maximum of three zeroes. This is because a cubic equation is a polynomial with a degree of three, meaning it can have a maximum of three solutions.

5. How do you know if a cubic equation has complex solutions?

A cubic equation will have complex solutions if the discriminant, b²-4ac, is negative. This means that the solutions will involve complex numbers, such as imaginary numbers. Graphically, this would result in the graph of the cubic equation not intersecting the x-axis at any real points.

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