Rational roots - standard form of equation

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SUMMARY

The discussion centers on transforming the equation 4x² + 2kx - k = 2x into standard form for the purpose of applying the quadratic formula to determine if the roots are rational. The correct standard form is achieved by rearranging the equation to 4x² + 2(k-1)x - k = 0. This transformation involves subtracting 2x from both sides of the equation, which simplifies the expression and allows for the application of the discriminant formula Δ = b² - 4ac.

PREREQUISITES
  • Understanding of quadratic equations and their standard forms
  • Familiarity with the quadratic formula and discriminant
  • Basic algebraic manipulation skills
  • Knowledge of rational roots and their significance
NEXT STEPS
  • Study the derivation and application of the quadratic formula
  • Learn about the discriminant and its role in determining the nature of roots
  • Explore examples of converting various polynomial equations to standard form
  • Investigate rational root theorem and its applications in polynomial equations
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Students preparing for algebra exams, educators teaching quadratic equations, and anyone seeking to improve their understanding of polynomial transformations and rational roots.

Janinever
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Hi everybody!

I've hit a blank with regards to this 1 equation on a old exam paper - think I've overloaded myself a bit and just feel a bit like a airhead at the moment!

I understand the actual method and getting to the answer but it starts off with a equation which you then need to get to a standard form to use the formula to check if the roots are rational.

The initial equation is this :

4x^2 + 2kx - k = 2x

Then on the memorandum this is taken to standard form so the info can be substituted into the formula Δ = b^2 - 4ac

the standard form they then write that initial equation in is :

4x^2 + 2(k-1)x-k = 0

How do they get from 4x^2 + 2kx - k = 2x to this 4x^2 + 2(k-1)x-k = 0

The rest I understand entirely. Literally just the above has be scratching my head!

Please help :)

Thank you!
 
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Janinever said:
How do they get from 4x^2 + 2kx - k = 2x to this 4x^2 + 2(k-1)x-k = 0

Sometimes you overlook the obvious answers. Just subtract 2x from both sides.
 
Thank you!
 

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