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Complex numbers can represent real world data, in a way that may be more complicated (or near impossible), if trying to represent with just real numbers. I cannot post links in the answer, but recently the Numberphile channel on YouTube posted a video on Quaternions. Also there used to be a really cool article with an interactive animation, showing what imaginary numbers represent on (picomonster dot com) but it no longer works.
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What equation could generate 5 real and 2 complex number solutions?
x^7 + 15x^6 + 86x^5 + 240x^4 + 359x^3 + 345x^2 + 274x + 120 = 0
What is the quadratic equation of x2 equals -11 using the complex number system?
13
How do you determine the number of solutions of an equation?
the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
How can you tell when an equation in one variable has infinitely many solutions or no solutions?
There is no simple method. The answer depends partly on the variable's domain. For example, 2x = 3 has no solution is x must be an integer, or y^2 = -9 has no solution if y must be a real number but if it can be a complex number, it has 2 solutions.
How many solution will there be if the quadratic equation does not touch or cross the x-axis?
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
What equation could generate 5 real and 2 complex number solutions?
x^7 + 15x^6 + 86x^5 + 240x^4 + 359x^3 + 345x^2 + 274x + 120 = 0
How do you recognize when an equation has no real solution or an infinite number of solutions?
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
How many solutions does the equation have?
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
What is the quadratic equation of x2 equals -11 using the complex number system?
13
How do you determine the number of solutions of an equation?
the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
Why does 14.8 have 2 solutions?
It does not have any solutions! 14.8 is a number, not an equation, inequality or question and so has no solutions.
What number is basic solution?
The basic solution is typically the simplest solution to a problem or equation, typically the starting point for more complex solutions. It is not a specific numerical value.
Why don't all rational equations have a single solution?
The number of solutions of a rational equation depends on the power (or degree) of the equation (that is, the highest power to which the variable is raised) and the domain. In the complex domain, each rational equation of power n has n solutions. It is, however, possible that two or more of these solutions are coincident - or "multiple zeros". In the real domain, the number of solutions can fall in pairs. So an equation of power 7 will always have 7 complex solutions but it can have 7, 5, 3 or 1 real solutions. (Real numbers are a subset of complex numbers). Another way of seeing this is through factorisation: The equation x3 + x2 - 10x + 8 = 0 can be factorised into (x + 1)*(x - 2)*(x - 4) = 0 Now the product of three numbers is 0 is any one of them is 0. That is, if x + 1 = 0 or if x - 2 = 0 or if x - 4 = 0 Thus the equation has the solutions: x = - 1, x = 2 or x = 4. The equation of order n can have at most n real binomial factors. (Any more and the biggest power of x would be bigger than n). And again, in the complex domain, using the binomial equation (and equivalents), it must have n binomial factors.
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
How can you determine the number of solutions for an equation?
The number of solutions for an equation can be determined by analyzing the degree of the equation and its graphical representation. For a linear equation, there is either one solution (if the lines intersect) or no solution (if the lines are parallel). Quadratic equations can have two solutions, one solution, or no real solution, depending on the discriminant. Higher degree equations can have multiple solutions or no solutions depending on the nature of the equation.
In general how many distinct solutions are there to a quadratic equation?
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
