How many real-number solutions does the equation have?
0 equals negative 5 x squared plus 8x minus 7
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
C. no solutions
To determine the number of real-number solutions for the equation, we can use the discriminant. The discriminant is given by the formula:
D = b^2 - 4ac
Where a, b, and c are the coefficients of the equation in the form ax^2 + bx + c = 0.
In this case, the equation is -5x^2 + 8x - 7 = 0, so we can identify the coefficients:
a = -5
b = 8
c = -7
Now we can substitute these values into the discriminant formula:
D = (8)^2 - 4(-5)(-7)
Simplifying further:
D = 64 - 140
D = -76
The discriminant is negative (-76), which means there are no real-number solutions. Therefore, the answer is C. no solutions.