How do I determine the real number solution for the following problem: The problem reads : Determine the number of real-number solutions to the equation from the given graph. x^2 - x + 15 = 0, given the graph of y = x^2 - x + 15
For any quadratic of the form
ax^2 + bx + c = 0 , evaluate b^2 - 4ac
if b^2 - 4ac > 0 , there will be 2 distinct real roots
if b^2 - 4ac < 0 there will be 2 complex roots
if b^2 - 4ac = 0 there will be one real roots, (actually two equal roots)
so in your case
b^2 - 4ac = 1 - 4(1)(15) = -59
So there are no real roots.
ty
To determine the number of real-number solutions to the equation x^2 - x + 15 = 0, given the graph of y = x^2 - x + 15, we need to examine the graph and analyze its behavior.
Step 1: Plot the graph of the equation y = x^2 - x + 15. This can be done by using a graphing tool or by plugging in different x-values and calculating the corresponding y-values.
Step 2: Observe the graph and examine the y-values. Look for the points where the graph intersects or touches the x-axis (the line y = 0). These are the x-values that satisfy the equation x^2 - x + 15 = 0.
Step 3: Count the number of intersection points or places where the graph touches the x-axis. This will give us the number of real-number solutions to the equation.
If there are no intersection points or places where the graph touches the x-axis, then there are no real-number solutions to the equation.
If there is one intersection point or one place where the graph touches the x-axis, then there is exactly one real-number solution to the equation.
If there are two intersection points or two places where the graph touches the x-axis, then there are exactly two real-number solutions to the equation.
If there are more than two intersection points or places where the graph touches the x-axis, then there are more than two real-number solutions to the equation.
By following these steps and analyzing the graph of y = x^2 - x + 15, you can determine the number of real-number solutions to the equation x^2 - x + 15 = 0.