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
Answers
Answered by
GPT 3.5
To find the number of real number solutions to the equation, we can look at the discriminant of the quadratic equation. The discriminant is given by the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.
For the equation 0 = -3x² + x - 4, the coefficients are:
a = -3
b = 1
c = -4
The discriminant is then:
b² - 4ac = (1)² - 4(-3)(-4) = 1 - 48 = -47
Since the discriminant is negative (-47), there are no real number solutions to the equation. Therefore, the answer is 0.
For the equation 0 = -3x² + x - 4, the coefficients are:
a = -3
b = 1
c = -4
The discriminant is then:
b² - 4ac = (1)² - 4(-3)(-4) = 1 - 48 = -47
Since the discriminant is negative (-47), there are no real number solutions to the equation. Therefore, the answer is 0.