Question

determine the discriminant for the quadratic equation –3 = x2 4x 1. based on the discriminant value, how many real number solutions does the equation have? discriminant = b2 – 4ac real number solutions

Answer 1

The discriminant of the quadratic equation is 24, which indicates that there are two real number solutions.

Step-by-step explanation:

To determine the discriminant for the quadratic equation – the equation must first be written in the standard form ax²+bx+c=0. The given equation appears to have a typo, but it seems to represent x² + 4x + 1 = 3. By rearranging it, we obtain x² + 4x - 2 = 0, where a=1, b=4, and c=-2. Now, we calculate the discriminant using the formula b² - 4ac, which equals 4² - 4(1)(-2) = 16 + 8 = 24.

Since the discriminant is positive, this indicates that the quadratic equation has two real number solutions.

Answer 2

x^2 + 4x + 4 = 0
d = b^2 - 4ac, where a = 1, b = 4 and c = 4
d = 4^2 - 4 x 1 x 4
d = 16 - 16 = 0
Since d = 0, there is one real solution to the equation.