The root of an equation is a value that satisfies the equation when substituted for the variable in place of an unknown variable.
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The root of an equation refers to the values of the variable that make the equation true. In other words, it is the value of the variable that satisfies the equation. This is also known as a solution of the equation. For example, in the equation x² – 4 = 0, the roots are 2 and -2, because when those values are substituted for x, the equation is true.
According to John Forbes Nash Jr., a renowned American mathematician, “Mathematics is the study of the structure that comes from the investigation of equations.”
Facts about roots include:
- An equation may have one or more roots, depending on the degree of the equation.
- The degree of the equation refers to the highest exponent of the variable in the equation.
- Linear equations (degree one) will always have exactly one root, unless the equation is inconsistent or has no solution.
- Quadratic equations (degree two) may have two roots, one root or no roots.
- Higher-degree polynomials may have several roots, including complex roots.
A table can also be used to illustrate the roots of an equation:
Equation Root(s)
x + 1 = 0 -1
2x² + 5x – 3 = 0 x = -3, x = 1/2
3x³ – 18x² + 27x = 0 x = 0, x = 3, x = 6
Understanding the roots of an equation is fundamental to solving problems in mathematics, science, and engineering.
This video contains the answer to your query
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 ‘x’ in the equation for which the equation holds true. In other words, the roots of a quadratic equation are the values of ‘x’ where the graph of the quadratic equation cuts the x-axis. For any given quadratic equation, there can only be 0, 1, or 2 roots.
Solution to an equation
root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.
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Similarly, What is an example of root of an equation?
For example, the roots of the quadratic equation x2 – 7x + 10 = 0 are x = 2 and x = 5 because they satisfy the equation. i.e., when each of them is substituted in the given equation we get 0. when x = 2, 22 – 7(2) + 10 = 4 – 14 + 10 = 0.
Besides, How do you find the root of an equation? As an answer to this: And x plus one equals zero. Then you just solve for your variable. And that is how you find the roots in the of. The equation.
Likewise, What is another word for root of an equation?
In reply to that: Answer: Roots are also called x-intercepts or zeros.
Keeping this in consideration, What is a root in an expression?
In reply to that: The root of an expression is the reverse of raising it to a power: An expression raised to the second power is equal to that expression multiplied by itself 2 times.
How do I find all the roots of an equation? 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? 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.
Subsequently, Does the equation have two roots? As a response 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.
How do I find all the roots of an equation?
The response is: 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?
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.
Secondly, Does the equation have two roots?
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.