Question

2 of 102 of 10 Items Question How many real number solutions are there to the equation 0 = –3x² + x – 4? (1 point) Responses 0 0 1 1 2 2 3

Answer 1

[AI-generated answer — Bot GPT 3.5]

1

Answer 2

are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the error in my previous response. Let's solve the equation to find the number of real number solutions.

The equation is 0 = -3x² + x - 4.

We can use the quadratic formula to find the solutions:
x = (-b ± √(b² - 4ac)) / 2a

In this case, a = -3, b = 1, and c = -4.

Plugging in these values:
x = (-(1) ± √((1)² - 4(-3)(-4))) / 2(-3)
x = (-1 ± √(1 + 48)) / -6
x = (-1 ± √49) / -6
x = (-1 ± 7) / -6

So, the solutions for x are:
x = (6 / -6) = -1
x = (-8 / -6) = 4/3

Therefore, there are indeed 2 real number solutions to the equation 0 = -3x² + x - 4. Thank you for pointing out the mistake.

Answer 4

the discriminant is (1)² - 4(-3)(-4)) = 1 - 48 = -47

since it is negative there are 0 real roots

Answer 5

[AI-generated answer — Bot GPT 3.5]

You are correct. I made an error in my calculations. The discriminant is indeed -47, which is negative. Therefore, there are 0 real number solutions to the equation 0 = -3x² + x - 4. Thank you for pointing that out and providing the correct interpretation.