Rational roots - standard form of equation

In summary, the conversation revolved around a question about converting an initial equation to standard form in order to use a formula for checking rational roots. The initial equation was given as 4x^2 + 2kx - k = 2x, and the standard form was written as 4x^2 + 2(k-1)x - k = 0. The answer to the question was to simply subtract 2x from both sides.
  • #1
Janinever
13
0
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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  • #2
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.
 
  • #3
Thank you!
 

What is the standard form of an equation with rational roots?

The standard form of an equation with rational roots is a polynomial equation in which the coefficients are integers and the exponents are non-negative integers.

How do you determine if an equation has rational roots?

To determine if an equation has rational roots, you can use the Rational Root Theorem, which states that if the coefficients of a polynomial equation are integers, then any rational roots must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

What is the process for finding rational roots of an equation?

The first step in finding rational roots of an equation is to list all possible factors of the constant term and the leading coefficient. Then, using the Rational Root Theorem, you can test each of these factors by plugging them into the equation. If one of the factors satisfies the equation, then it is a rational root.

Can an equation have irrational roots if it is in standard form with rational roots?

Yes, an equation can have irrational roots even if it is in standard form with rational roots. This is because the Rational Root Theorem only guarantees that rational roots will be in the form of p/q, but it does not rule out the possibility of irrational roots.

What is the significance of finding rational roots in an equation?

Finding rational roots in an equation can help in solving the equation, as it narrows down the possible solutions. It also provides a deeper understanding of the equation and its behavior, as rational roots can give insight into the symmetry and behavior of the graph of the equation.

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