How many real-number solutions does the equation have?
-7x^2 + 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, which is the part of the quadratic formula under the square root symbol.
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / (2a)
In the equation -7x^2 + 6x + 3 = 0, a = -7, b = 6, and c = 3.
The discriminant is calculated by: b^2 - 4ac
Substituting the values into the discriminant formula, we have: (6)^2 - 4(-7)(3)
Simplifying, we get: 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.