if a and b are the roots of the equation x^2-3x+1=0, what is the value of
(1/a) + (1/b)?
If the function f is defined by f(x) = (x-1)^2 -3, where -1 is less than or equal to x and 3 is greater than or equal to x. Which of the following is the range of f?
using the properties of roots,
a+b = 3
ab = 1
(1/a + 1/b)
= (a+b)/(ab) = 3/1 = 3
for the 2nd, "Which of the following .."
I don't see any "following"
To find the value of (1/a) + (1/b), we can use the fact that if a and b are the roots of a quadratic equation, then the quadratic equation can be written as (x - a)(x - b) = 0.
In this case, the quadratic equation is x^2 - 3x + 1 = 0. So we can use the formula (1/a) + (1/b) = -(coefficient of x term)/(constant term), which gives us -(3/1) = -3.
Therefore, the value of (1/a) + (1/b) is -3.
Now, let's look at the function f(x) = (x-1)^2 - 3. To determine the range of this function, we need to find the minimum value of f(x).
Since (x - 1)^2 is always non-negative, the minimum value of f(x) occurs when (x - 1)^2 = 0. This happens when x = 1.
Substituting x = 1 into the expression f(x) = (x-1)^2 - 3, we get f(1) = (1-1)^2 - 3 = -3.
Therefore, the range of the function f is {-3}.