SOLUTION: Use the discriminant to determine how many real-number roots the equation has. Do not solve the equation. x^2-3x+5=0 That's what the worksheet says but I have no idea what a di

Click here to see ALL problems on Quadratic Equations

Question 7117: Use the discriminant to determine how many real-number roots the equation has. Do not solve the equation.
x^2-3x+5=0
That's what the worksheet says but I have no idea what a discriminant is or how to use it to determine how many real-number roots the equation has. What are real-number roots? Thank you to the tutors who help me with this.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Perhaps a little review is in order.
One of the ways to solve quadratic equations is by employing the "quadratic formula":

To use this formula however, the quadratic equation must be in "standard form":

Your equation is already in standard form.
What is the discriminant? It's that part of the quadratic formula under the square root sign:
If the discriminant is positive, the solution has two real roots.
If the discriminant is negative, the solution has two complex conjugate roots.
If the discriminant is zero, the solution has one real root, but this is really a double root.
Let's look at the discriminant of your equation,
The discriminant is: = -11
The discriminant is negative, so the solution has two complex conjugate roots.
To interpret this result graphically, the parabola represented by your quadratic equation opens upwards (coefficient of x^2 is positive) and the parabola does not cross the x-axis. See the graph below: