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