## anonymous one year ago Calculate the discriminant to determine the number of real roots. y = x2 + 3x + 9 How many real roots does the equation have? (Points : 5) one real root two real roots no real roots no solution to the equation

1. anonymous

i think its between A or B @Nnesha

2. mathstudent55

Do you know what the discriminant is?

3. anonymous

no @mathstudent55

4. mathstudent55

|dw:1434495669530:dw|

5. mathstudent55

The drawing above shows the quadratic formula. It is used to solve quadratic equations.

6. anonymous

ok

7. mathstudent55

|dw:1434495759652:dw|

8. mathstudent55

The discriminant is the part inside the square root symbol. It is the part inside the rectangle.

9. anonymous

ok im starting to understand @mathstudent55

10. mathstudent55

If you have an equation of the form \(ax^2 + bx + c = 0\), you can use the quadratic formula to solve it. Before you even solve it, you can just evaluate the discriminant to find out the nature of the solutions. If the discriminant is positive, there are two real solutions. If the discriminant equals zero, there are two equal real solutions. If the discriminant is negative, there are two complex (imaginary) solutions.

11. mathstudent55

Your problem is: y = x2 + 3x + 9 We set the right side equal to zero, and now we have a quadratic equation. \(x^2 + 3x + 9 = 0\)

12. mathstudent55

If you compare your equation to \(ax^2 + bx + c = 0\) you see that in your equation, a = 1, b = 3, and c = 9.

13. mathstudent55

|dw:1434496073864:dw|

14. mathstudent55

|dw:1434496111258:dw|

15. mathstudent55

Now we use those values of a, b, and c in the discriminant to see what type of quadratic equation you have.

16. mathstudent55

|dw:1434496200738:dw|

17. mathstudent55

We see that the discriminant is a negative number. Now you can look above to find out what a negative discriminant tells you about the solutions of the quadratic equation.