How many real number solutions does the equation have?
0=-5x^(2)+8x-7
This equation has no real number solutions.
To see why, we can use the discriminant of the quadratic formula:
b^2 - 4ac
For the equation 0=-5x^(2)+8x-7, a=-5, b=8, and c=-7. Substituting in these values, we get:
8^2 - 4(-5)(-7) = 8^2 - 140 = -56
Since the discriminant is negative, the quadratic equation has no real number solutions.
To determine the number of real number solutions for the equation 0 = -5x^2 + 8x - 7, we can analyze the discriminant of the quadratic equation.
The discriminant (b^2 - 4ac) provides information about the nature and number of solutions of a quadratic equation in the form ax^2 + bx + c = 0.
In this case, the quadratic equation is -5x^2 + 8x - 7 = 0, so we have:
a = -5, b = 8, c = -7.
The discriminant can be calculated as follows:
D = b^2 - 4ac
= (8)^2 - 4(-5)(-7)
Simplifying:
D = 64 - 140
= -76
The value of the discriminant D is negative (-76). When the discriminant is negative, it means that the quadratic equation has no real number solutions.
Therefore, the equation 0 = -5x^2 + 8x - 7 has no real number solutions.