Determine the number of real-number solutions to the equation
-2x2 - x - 5 = 0, given the graph of y = -2x2 - x - 5
You have to use the discriminant to find the real number solutions. discriminant=b^2-4ac
a=-2, b=-1, c=-5 (the co-efficients from your equation, in order)
1-4(-2)(-5)=1-40=-39
Since it came out to -39, there are no real number solutions (because it is negative). When the answer is positive, there are two real number solutions. When the answer is zero, there is one real number solution.
To determine the number of real-number solutions to the equation -2x^2 - x - 5 = 0, we can look at the graph of the equation y = -2x^2 - x - 5.
Step 1: Graph the equation y = -2x^2 - x - 5.
To graph the equation, we plot points that satisfy the equation and connect them. However, due to the nature of this quadratic equation, it is more efficient to use the properties of the graph to determine the number of real-number solutions.
The graph of a quadratic equation in the form y = ax^2 + bx + c is a parabola. In this case, since the coefficient of x^2 is negative (-2), the parabola opens downwards.
Step 2: Determine the number of real solutions.
Since the parabola opens downwards, it intersects the x-axis at most twice. If the parabola does not touch or intersect the x-axis, then there are no real solutions. If it touches the x-axis at one point, then there is one real solution. If it intersects the x-axis at two different points, then there are two real solutions.
Step 3: Analyze the graph.
Look at the graph and see if it intersects or touches the x-axis. Based on the graph, we can observe that the parabola intersects the x-axis at two different points.
Therefore, there are two real-number solutions to the equation -2x^2 - x - 5 = 0.