How do you know if there is only one solution?
A system of linear equations has one solution when the graphs intersect at a point. No solution. A system of linear equations has no solution when the graphs are parallel.
How do you know that a quadratic equation has only one solution?
Quadratic equations have one solution when the vertex of the parabola just touches the x axis,, or the line y=0. These equation can be written as (x+a)(x+a), because when we solve each of these brackets both give us the solution -a, so therefore there is only one solution.
How many solutions does x2 have?
X^2=n in the set of real numbers it has infinitely many solutions for assuming n positive or zero x=sqrt(n) and for a positive or zero n the function x=sqrt(n) is unbounded. So the range is [0,infinity[ which means infinite number of solutions.
Why does 2 x have no solution?
The equation x squared = -2 has no Real solution. No number times itself will ever equal -2, so there is no solution.
What is a one solution?
What is the definition of one solution? no matter what constant is substituted in for the variable, the equation is ALWAYS true. no matter what constant is substituted in for the variable, the equation will NEVER be true. only this ONE solution will make the equation true.
Which system has exactly one solution?
independent system
An independent system has exactly one solution pair (x,y) . The point where the two lines intersect is the only solution. An inconsistent system has no solution.
What is a quadratic equation with 2 solutions?
The discriminant is negative, so the quadratic equation has two complex solutions. The quadratic equation x2 – 4x + 10 = 0 has two complex solutions. Suppose a quadratic equation has a discriminant that evaluates to zero….
| x = −1 + 2i | x = −1 – 2i |
|---|---|
| 1 – 4 – 2 = −5 | 1 – 4 – 2 = −5 |
| −5 = −5 | −5 = −5 |
Which equation has no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
How many solutions are there?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
How many solutions does this quadratic have?
2 solutions
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero.
What equation has two solutions?
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
What is sqrt(x^2) = |x|?
|x| equals x if x>0 and -x otherwise. Therefore, sqrt (x^2) = |x|. Pedantic, yes, but this is a definition, not a deep fact. You just have to understand the meaning of the word “definition”.
Is the square root function the inverse of x^2×2 for all real numbers?
Reply: The square root function is not the inverse of x 2 x^2 x 2 for all real numbers. Instead, it is an inverse of x 2 x^2 x 2 only on the interval [ 0, ∞) [0, \\infty) [ 0, ∞). Here is a graph of the square-root function.
What is the principle root of x^2 = 4?
The square root function gives the “principle root”. Since there are two solutions to the equation x^2 = 4, namely 2 and -2 then in order that sqrt be a function (have a unique value) we must pick one of the two solutions. We adopt the convention of choosing the positive solution and call this the “principle” solution.
Are |X| and sqrt(x^2) identical on the real numbers?
The functions |x| and sqrt (x^2) are identical on the real numbers, and that is an immediate consequence of the definition of each. It is not a deep fact, and it requires nothing that really merits the word ‘proof’.