How many real number solutions does the equation have? y=-5x^2+8x-7
There would be an infinite number of solutions.
Any ordered pair that satisfies the equation would be a solution.
If you meant: How many real number solutions does the equation 0 = -5x^2+8x-7 have?
There would be no real solution, see ...
http://www.wolframalpha.com/input/?i=y%3D-5x%5E2%2B8x-7
Well, to find the number of real solutions, we can use a quadratic equation. Let's call your equation y = -5x^2 + 8x - 7. If we put this in the form of ax^2 + bx + c = 0, we get -5x^2 + 8x - 7 = 0. Now, you may be wondering, "how did we go from the equation y = -5x^2 + 8x - 7 to -5x^2 + 8x - 7 = 0?" Well, in order to find solutions, we need to set y equal to zero.
Now, to determine the number of real solutions, we can use the discriminant formula, which is the b^2 - 4ac part of the quadratic formula. In our case, a = -5, b = 8, and c = -7. Substituting those values, we get b^2 - 4ac = 8^2 - 4(-5)(-7) = 64 - 140 = -76.
Uh oh! The discriminant is negative, which means that the equation has no real solutions. But hey, don't be sad! At least the equation didn't give us zero solutions – it gave us (negative) punfinite solutions!
To find the number of real number solutions for the equation y = -5x^2 + 8x - 7, we need to determine the discriminant of the quadratic equation.
The discriminant, denoted as Δ, is given by the formula: Δ = b^2 - 4ac, where a, b, and c are the coefficients in the equation in the form ax^2 + bx + c.
In this case, a = -5, b = 8, and c = -7. Plugging these values into the formula, we get:
Δ = (8)^2 - 4(-5)(-7)
= 64 - 140
= -76
Since the discriminant is negative (Δ < 0), this means that the equation y = -5x^2 + 8x - 7 has no real number solutions.
To determine the number of real number solutions for the equation y = -5x^2 + 8x - 7, we can analyze the discriminant of the quadratic equation.
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. In our case, a = -5, b = 8, and c = -7.
The discriminant (D) of a quadratic equation is given by the formula D = b^2 - 4ac.
Substituting the values from our equation, we have:
D = (8)^2 - 4(-5)(-7)
= 64 - 140
= -76
Since the discriminant is negative (D < 0), it means that the quadratic equation does not have any real number solutions.
Therefore, the equation y = -5x^2 + 8x - 7 does not have any real number solutions.