Question

Suppose that a and b are nonzero real numbers, and that the equation {x²+ ax + b = 0} has solutions a and b. Then what is the pair (a,b)?

Answer 1

The pair (a,b) for the equation x² + ax + b = 0 is (±√(-b/2), -b/8).

Step-by-step explanation:

To find the pair (a,b) for the equation x² + ax + b = 0, we need to apply the quadratic formula. In this case, the quadratic formula is:

x = (-a ± √(a² - 4b)) / 2

Since the equation has solutions a and b, we can equate them to the values of x from the quadratic formula:

a = (-a ± √(a² - 4b)) / 2

By simplifying the equation and isolating the variables, we can find the pair (a,b):

2a = -a ± √(a² - 4b)

3a = ± √(a² - 4b)

Squaring both sides:

9a² = a² - 4b

8a² = -4b

a² = -b/2

Thus, the pair (a,b) is (±√(-b/2), -b/8).