Write answer with only one root

Thread starter fhs1989
Start date Aug 5, 2012
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In summary, "write answer with only one root" means to find a single value that satisfies the equation when solving for its roots. It is important to have only one root in an answer because it indicates a unique solution and avoids confusion or errors. An equation with only one root will have a single point where the graph crosses the x-axis and a leading coefficient of 1. Strategies for writing an answer with only one root include using the quadratic formula and factoring the equation. However, an equation can have more than one root, including two roots for a quadratic equation. It is necessary to carefully analyze the equation and its graph to determine the number of roots it has.

Aug 5, 2012

fhs1989

Homework Statement

At the end I get the answer: sqrt(sqrt(3)+2)

It can be show that it is ( sqrt(6)+sqrt(2) ) / 2

How do I show this?, I have tried, to attempt it my manipulating the expression, but I can't seem to manage it.

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Aug 5, 2012

stgermaine

((sqrt(6)+sqrt(2)) / 2)^2 = (1/4)(6+2*sqrt(2)*sqrt(6) + 2) = (1/4)(8 + 2sqrt(12)) = 1/4(8 + 4sqrt(3)) = sqrt(3) + 2

FAQ: Write answer with only one root

What does "write answer with only one root" mean?

When solving for the roots of a mathematical equation, the term "root" refers to the value that makes the equation equal to zero. In this context, "write answer with only one root" means to find a single value that satisfies the equation.

Why is it important to have only one root in an answer?

Having only one root in an answer is important because it means the equation has a unique solution. This is necessary for accurately solving real-world problems and avoiding any confusion or errors that may arise from multiple solutions.

How can I determine if an equation has only one root?

An equation with only one root will have a single point where the graph crosses the x-axis. This means that when graphed, the equation will intersect the x-axis at only one point. Additionally, an equation with a leading coefficient of 1 will always have only one root.

What strategies can I use to write an answer with only one root?

One strategy for finding an answer with only one root is to use the quadratic formula. This formula is specifically designed to solve quadratic equations with one root. Additionally, you can factor the equation to find the roots and determine if there is only one solution.

Can an equation have more than one root?

Yes, an equation can have multiple roots. For example, a quadratic equation can have two roots. However, there may be some cases where the equation has no real roots or an infinite number of roots. It is important to carefully analyze the equation and its graph to determine the number of roots it has.