What function would have a zero at sqrt2?
To find a function that has a zero at √2, we can start by thinking about the properties of zeros. In mathematics, a zero of a function, also known as a root, is a value for which the function evaluates to zero.
One way to create a function with a zero at √2 is by using the concept of roots. Since √2 is a square root, we can express it as the solution to the equation x^2 - 2 = 0.
By rearranging the equation, we get x^2 = 2. Taking the square root on both sides, we find x = ±√2. This means that the function has two distinct zeros: √2 and -√2.
Therefore, a quadratic function that has a zero at √2 is f(x) = x^2 - 2.
To verify that this function indeed has a zero at √2, we can substitute √2 into the function:
f(√2) = (√2)^2 - 2
= 2 - 2
= 0
As expected, when we substitute √2 into the function, we get a result of zero, confirming that √2 is a zero of the function f(x) = x^2 - 2.