How many real-number solutions does the equation have?
–7x2 + 6x + 3 = 0
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
B. two solutions
To determine the number of real-number solutions for the equation -7x^2 + 6x + 3 = 0, we can use the discriminant.
The discriminant is given by the formula: b^2 - 4ac, where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
In this case, a = -7, b = 6, and c = 3. Plugging these values into the discriminant formula, we have:
discriminant = (6)^2 - 4(-7)(3)
= 36 + 84
= 120
Since the discriminant is positive (120 > 0), the equation has two distinct real-number solutions.
Therefore, the answer is B. two solutions.