Factoring and Plotting a Polar Equation

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Homework Help Overview

The discussion revolves around factoring and plotting a polar equation, specifically the expression r^2 - r + (1/4)sin^2(4θ). Participants are trying to clarify the nature of the equation and the steps needed to factor it.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants question whether the expression is indeed an equation due to the absence of an equal sign. There are discussions about the possibility of factoring the expression and the conditions under which it can be factored, including references to roots and the quadratic formula.

Discussion Status

The discussion is active, with participants exploring different interpretations of the expression and its requirements for factoring. Some guidance has been offered regarding the use of the quadratic formula to find roots, although there is no consensus on the factoring process itself.

Contextual Notes

There is uncertainty regarding the proper formulation of the equation, specifically whether it should equal zero, which affects the factoring discussion. Participants are also navigating the implications of working with polar equations.

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Homework Statement



The question is: Factor and Plot the polar equation
r^2-r+(1/4)sin^2 4 theta

Homework Equations



N/A

The Attempt at a Solution



I have no idea how to do this.
 
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r^2-r+(1/4)sin^2 4 theta is not an equation because there's no equal sign. Is it supposed to equal 0? If so, do you know how to factor a quadratic equation?
 
yes it equals 0
how am i supposed to factor this?
 
You can't. Are you sure it isn't [itex]r^2- r(1/4)sin^2(4\theta)[/itex]?
 
You can factor it. Does it make sense that if a and b are the roots of the equation, r^2-r+(1/4)sin^2 4 theta can be factored into A(r-a)(r-b)? You can find a and b using the quadratic formula. You won't get a numerical answer, but you will get an expression for a and b in terms of theta.
 

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