Find when 2x^3+x-5 is equal to zero

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In summary, the conversation discusses finding the value of x when the polynomial 2x^3+x-5 is equal to zero. The person is stuck and suggests using a theorem for finding rational zeroes, but the other person mentions that Hurkyl's method shows there are no rational solutions. They also mention a "cubic formula" but suggest solving numerically or graphing on a calculator to find the x-intercept.
  • #1
UrbanXrisis
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I need to find when 2x^3+x-5 is equal to zero and I'm stuck

2x^3+x-5=0
5=2x^3+x...then what?
 
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  • #2
You sure you have the right problem?


There is a really nice theorem for finding all of the rational zeroes of a polynomial that involves the first and last terms of the polynomial, have you seen it yet?
 
  • #3
Hurkyls method show that there are no rational solutions. That means that this cannot be factored with integer coefficients. There is a "cubic formula" but it is very messy. It is probably best solved numerically.

(The method I used was to graph it on my calculator, then "zoom" in on the x-intercept!)
 

FAQ: Find when 2x^3+x-5 is equal to zero

What is the formula for solving for when 2x^3+x-5 is equal to zero?

The formula for solving this equation is known as the quadratic formula, which is (-b ± √(b^2-4ac)) / 2a. In this case, a=2, b=1, and c=-5.

What is the degree of this equation?

The degree of this equation is 3, since the highest exponent is 3.

What are the possible solutions for this equation?

The possible solutions for this equation can be found by plugging in the values of a, b, and c into the quadratic formula and solving for x. In this case, the possible solutions are -1.618 and 1.118.

How can I check if my solutions are correct?

You can check your solutions by plugging them back into the original equation and seeing if they make the equation equal to zero. Additionally, you can use a graphing calculator to plot the equation and see if the solutions intersect with the x-axis.

Are there any other methods for solving this equation?

Yes, there are other methods such as factoring or using the Rational Roots Theorem. However, the quadratic formula is the most reliable and efficient method for solving this type of equation.

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