What is the General form of this equation? (x- -1)^2 +(y-1)^2 =225.0
1 answer:
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Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in ,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is
where is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with . For convenience write
. This gives the factor
. Hence,
Notice that . So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is
Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.
Answer:
1 solution
Step-by-step explanation:
Jeremy can simplify the equation enough to determine if the x-coefficient on one side of the equation is the same or different from the x-coefficient on the other side. Here, that simplification is ...
-3x -3 +3x = -3x +3 +3
We see that the x-coefficient on the left is 0; on the right, it is -3. These values are different, so there is one solution.
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In the attached, the left-side expression is called y1; the right-side expression is called y2. The two expressions are equal where the lines they represent intersect. That point of intersection is x=3. (For that value of x, both sides of the equation have a value of -3.)
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<em>Additional comment</em>
If the equation's x-coefficients were the same, we'd have to look at the constants. If they're the same, there are an infinite number of solutions. If they are different, there are no solutions.
