Kulla_9289
Junior Member
- Joined
- Apr 18, 2022
- Messages
- 217
I would presume they expect you to find something you can draw on the graph such that its intersection(s) would be the solution(s) to the cubic equation.Use the graph of y=2/x^2 - x below to solve the equation 4x^3-10x^2+2=0. I literally have no idea as to what to do.
Finding solutions graphicallyAs the posting guideline ask, can you please tell us what topics you have recently learned?
How would I do that?I would presume they expect you to find something you can draw on the graph such that its intersection(s) would be the solution(s) to the cubic equation.
So, if you drew a line y = ax + b, what would it take for the equation 2/x^2 - x = ax + b to be equivalent to 4x^3 - 10x^2 + 2 = 0?
I can't be sure if that is what they have in mind, but it does work.
How would I do that?
[math]\frac{1}{x}=x \implies 1=x^2 \implies x^2-1=0[/math]Would you mind showing an example?
You need to multiply both entire sides by [imath]x^2[/imath], not just one term. So you want [imath](2/x^2-x)*x^2[/imath], that is, [math]\left(\frac{2}{x^2}-x\right)\cdot x^2[/math].How is [imath]2/x^2*x^2-x=2-x^3[/imath]? Isn't it [imath]2-x[/imath]?
Please elaborate. I do not understand why.2 -x^3 = ax^3 + bx^2 => (a+1)x^3 + bx^2 -2 =0 and Ax^3 + Bx^2 + D =0
Equate coefficients for (a+1)x^3 + bx^2 -2 and Ax^3 + Bx^2 + D
A=a+1, B =b and D=-2
You are given A, B and D
Continue
I'm not quite sure what you are saying here. To solve [imath]3x=1/2[/imath] you would not multiply (only) the right side by 2; you would multiply both sides by [imath]\frac{1}{3}[/imath] to isolate the variable by eliminating its coefficient.@Dr.Peterson So that's the rule. I haven't an idea as to why I have been taught [imath]3x=1/2*2[/imath] for [imath]3x=1/2[/imath] instead of [imath]3x=(1/2)*2[/imath]. These inconsistencies that have been impressed upon our minds are inextricable. Practises upon practises have been committed just to impress this upon our minds.
Makes sense now.
How are you doing on the problem as a whole? Which part of what Steven G (or others) said do you not understand?Please elaborate. I do not understand why.