An example of a root of an equation is x = 2 for the equation x² – 4 = 0.
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“The roots of an equation are the values of x that satisfy the equation when substituted,” as stated by MathIsFun. In other words, if an equation is represented as f(x) = 0, then the roots of the equation are the values of x that make f(x) equal to zero. An example of a root of an equation is x = 2 for the equation x² – 4 = 0. When x is substituted with 2, the equation becomes 2² – 4 = 0, which is true.
Interesting facts on the topic of roots of an equation include:
- An equation may have one or more roots, or it may have none.
- The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± sqrt(b² – 4ac)) / (2a).
- In some cases, the roots of an equation can be approximated using numerical methods, such as Newton’s method or the bisection method.
- The concept of finding roots of an equation is used in various areas of mathematics and science, including calculus, algebra, and physics.
- According to Albert Einstein, “Pure mathematics is in its way, the poetry of logical ideas.”
Here’s a table summarizing the roots of some common functions:
| Function | Roots |
|---|---|
| f(x) = x | x = 0 |
| f(x) = x² | x = 0 |
| f(x) = x³ | x = 0 |
| f(x) = sin(x) | x = nπ, where n is an integer |
| f(x) = cos(x) | x = (n+1/2)π, where n is an integer |
| f(x) = e^x | x = 0 |
| f(x) = ln(x) | x = 1 |
In summary, the roots of an equation are the values of x that make the equation true when substituted. It is a fundamental concept in mathematics and science and has various applications. As Sophie Germain once said, “I have no other wish than a continuation of the same application in the same spirit, believing that by doing so I shall thus deepen my own knowledge and, in general, advance the interests of science.”
See a related video
The video explains how to find the roots of a quadratic equation, using an example that is not in the standard form. The equation is first converted into the standard form and then the values of `a`, `b`, and `c` are determined. The two numbers that add up to `-8` and multiply to `-9` are found, and the equation is factored into `(x – 9)(x + 1) = 0`. Finally, by setting each parenthesis equal to zero and solving for `x`, the roots of the equation are found.
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The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation. For example, the roots of the quadratic equation x2 – 7x + 10 = 0 are x = 2 and x = 5 because they satisfy the equation.
The root of an equation is a value that makes the equation true when it is substituted for the unknown quantity. For example, 2 and 3 are roots of the equation 15 = x^2 + 2x because 15 = 2^2 + 2(2) and 15 = 3^2 + 2(3). An equation can have more than one root, depending on the degree of the polynomial. For instance, a quadratic equation has two roots, and a cubic equation has three roots.
Root of an equation (Alg.) that value which, substituted for the unknown quantity in an equation, satisfies the equation.
Roots of the equation are such values of the variable, that turn equation into correct equality. Example 1. Determine, whether 2 and 3 are roots of the equation {15}= { {x}}^ { {2}}+ {2} {x} 15 = x2 + 2x.
Root of an equation (Alg) that value which, substituted for the unknown quantity in an equation, satisfies the equation. Usage in scientific papers
The roots of an equation are the values that make it equal zero. If this is a regular polynomial, then that means there are as many factors (at least) as there are roots. So the equation is the product of three factors if there are three roots.
The inputs or values for the variables for which the equation gives 0 as the result are known as roots of the equation.
moreover we can write x^2+5x+6=(x+2)(x+3)=0
=%3E x+2=0 or x+3=0 ; so x=-2 or x=-3
for ex- x^2+5x+6=0 is an equation, then the only possible values of x are -2 and -3 for which the equation gives 0 result.
Moreover, people are interested
Also to know is, What is the root of an equation?
As a response to this: The roots of an equation is a fancy way of saying "solutions" of the equation. Solutions are the numerical values equal to the variable after solving it.
Thereof, How do you know if an equation has roots? The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots.
How do you solve roots of an equation? Answer to this: Though. I’m going to leave. It. I’m just going to show you i’m going to leave it as 26 over 4. Yes that is 6.5.
Hereof, Why find the root of an equation? Response will be: The purpose of finding roots is to find the range of a function this tells us the maximum and minimum value of a function and where on coordinate axis the graph meets.
How do I find all the roots of an equation? Response: The roots of any quadratic equation is given by: x = [-b +/- sqrt (-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the equation is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the roots of the equation are the values where the y axis is equal to 0.
What is the number of roots of the equation? Answer: The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots. Some methods for finding the roots are: All the quadratic equations with real roots can be factorized. The physical significance of the roots is that at the roots of an equation, the graph of the equation intersects x-axis.
Keeping this in consideration, Does the equation have two roots?
As an answer to this: This means the quadratic equation x 2 – 6x + 8 has two real roots, x = 2 and x = 4 (that is, both of the x values where the parabola and x axis intersect). Be careful: for a quadratic equation to have two real roots, its graph must touch the x axis twice.