Question

The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45. the actual roots ordered from least to greatest are and . partially factored form: f(x) = (x − 3)(x 3)(x2− 4x 5) use the quadratic formula to identify the zeroes of x2 − 4x 5.

Answer 1

The zeroes of the equation x² - 4x + 5 = 0 do not exist in the realm of real numbers.

Step-by-step explanation:

The quadratic formula can be used to find the zeroes of a quadratic equation of the form ax² + bx + c = 0. For the equation x² - 4x + 5 = 0, we can identify the values of a, b, and c as 1, -4, and 5 respectively. Plugging these values into the quadratic formula gives us:

x = (-b ± √(b² - 4ac))/(2a)

= (-(-4) ± √((-4)² - 4(1)(5)))/(2(1))

= (4 ± √(16-20))/2

= (4 ± √(-4))/2

Since there is a negative under the square root, we cannot take the square root of a negative number in the realm of real numbers. Therefore, there are no real roots for the equation x² - 4x + 5 = 0.