Answer:
To find the zeros of the quadratic equation x² - 4x + 5, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax² + bx + c = 0, the zeros can be found using the formula:
x = (-b ± √(b² - 4ac))/(2a)
In this case, the coefficients of the quadratic equation are a = 1, b = -4, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(1)(5)))/(2(1))
x = (4 ± √(16 - 20))/2
x = (4 ± √(-4))/2
Here, we have a square root of a negative number (√(-4)), which means that the zeros will be complex numbers. Let's simplify the equation further:
x = (4 ± 2i)/2
Now, we can simplify the expression by dividing both the numerator and denominator by 2:
x = 2 ± i
So, the zeros of the quadratic equation x² - 4x + 5 are:
x = 2 + i
x = 2 - i
These are the complex zeros of the equation.
Explanation: