find the roots of f(x)=x^2-1.5x+1
To find the roots of the quadratic equation f(x) = x^2 - 1.5x + 1, we can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation with the general quadratic equation, we have a = 1, b = -1.5, and c = 1. Plugging these values into the quadratic formula, we get:
x = (-(-1.5) ± √((-1.5)^2 - 4(1)(1))) / (2(1))
Simplifying further:
x = (1.5 ± √(2.25 - 4)) / 2
x = (1.5 ± √(-1.75)) / 2
Since the term inside the square root is negative, it means that there are no real roots for this quadratic equation. The solutions will be complex numbers.
Thus, the roots of f(x) = x^2 - 1.5x + 1 are complex numbers and can be expressed as:
x = (1.5 ± i√1.75) / 2, where i is the imaginary unit.