Given a polynomial equation p(x)=0, which expressions could be a pair of irrational roots of the equation?
please help I don't know how to solve this
Thank you for doing the other one I'm just really struggling with this. sorry to waste your time
I just did one for you
https://www.jiskha.com/display.cgi?id=1516928756#1516928756.1516930161
now if you want irrational roots
of a quadratic, what is b^2-4ac = 5
the sqrt 5 is irrational
so both roots will be irrational
now you could also use the rational roots theorem.
http://www.purplemath.com/modules/rtnlroot.htm
To determine which expressions could be a pair of irrational roots of the polynomial equation p(x) = 0, we first need to understand the concept of irrational numbers and their characteristics.
An irrational number is a real number that cannot be expressed as the ratio of two integers. It is a non-repeating, non-terminating decimal. Examples of irrational numbers include √2, √3, π, and e.
When solving a polynomial equation, we use various methods to find its roots. One common method is factoring, which is often useful for polynomials of low degrees. However, for higher degree polynomials, we usually rely on numerical approximation methods such as the Rational Root Theorem, synthetic division, or using calculators.
Since we don't have a specific polynomial equation, we cannot perform any direct calculations. However, we can evaluate expressions to check if they could represent irrational roots.
For example, let's take the expression x = √2. We can substitute this value into the equation and see if it satisfies the equation p(x) = 0. If it does, then √2 could be one of the irrational roots.
Alternatively, let's consider another expression x = π. Similar to the previous example, substitute this value into the equation p(x) = 0 and check if it satisfies the equation. If it does, then π could be another irrational root.
Keep in mind that there could be other expressions involving irrational numbers that could also satisfy the equation. The goal is to substitute these expressions into the given polynomial equation and verify if they yield a zero value.
Remember, the specific polynomial equation is essential to accurately determine the irrational roots.