Final answer:
If b² - 4ac > 0 and a non-perfect square, a quadratic equation has two real and distinct solutions.
Step-by-step explanation:
A quadratic equation in the form ax² + bx + c = 0 can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
In this case, if b² - 4ac > 0 and a is a non-perfect square, then the quadratic equation has two real and distinct solutions.
For example, if we have an equation like x² + 4x + 3 = 0, where a = 1, b = 4, and c = 3, then we can calculate the solutions using the quadratic formula:
x = (-4 ± √(4² - 4(1)(3)))/(2(1))
x = (-4 ± √(16 - 12))/(2)
x = (-4 ± √4)/(2)
x = (-4 ± 2)/(2)
Therefore, the solutions are x = -3 and x = -1.