How many roots does the equation y^2 = x^3 + x + 6 (mod 5 * 9^2) have?

In summary, finding the roots of a function means finding the values of x that make the function equal to zero. This is important in understanding the function's behavior and can be done through various methods such as factoring, using the quadratic formula, or graphing. A function can have multiple roots, but not all functions have real roots and this can be determined by examining the graph or the discriminant of a quadratic function.
  • #1
SneakyG
7
0
What are the 4 roots of a function y^2 = x^3 + x + 6 (mod 5 * 9^2)?

I don't know where to start a problem like this. The roots mod 5 are (0,1) (0,4) (2,1) (2,4) (3,1) (3,4) (4,2) (4,3) if that helps
 
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  • #2
is this a function of the form

g(x,y) = x^3 + x + 6 * (mod 5 * 9^2) - y^2
 
  • #3
I think it is meant to be in the form I posted
 
  • #4
What you posted is not a "function", it is an "equation". It would be equivalent to
f(x)= 0 where f is the function jedishrfu gave.
 

1. What is the meaning of finding roots of a function?

The roots of a function are the values of the independent variable (usually denoted as x) that make the function equal to zero. In other words, when the value of x is substituted into the function, the resulting output or y-value is zero.

2. Why is finding roots of a function important?

Finding the roots of a function is important because it helps us understand the behavior of the function. It allows us to identify important points on the graph such as intercepts, turning points, and relative extrema. Additionally, finding the roots can help us solve equations and make predictions about the function's behavior.

3. How do you find the roots of a function?

To find the roots of a function, we set the function equal to zero and solve for the value(s) of x that make the equation true. This can be done through various methods such as factoring, using the quadratic formula, or using numerical methods like Newton's method. Graphing the function can also help us estimate the roots.

4. Can a function have more than one root?

Yes, a function can have more than one root. In fact, a polynomial function of degree n can have up to n distinct roots. However, not all functions have real roots. Some functions may only have complex roots, while others may not have any roots at all.

5. How do you know if a function has no real roots?

A function has no real roots if the graph of the function does not intersect the x-axis. In other words, there are no values of x that make the function equal to zero. This can also be determined by examining the discriminant (b²-4ac) of a quadratic function. If the discriminant is negative, the function has no real roots. Additionally, if a function is always positive or always negative, it will not have any real roots.

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