9.2 THE DISCRIMINANT. The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,.

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Presentation transcript:

9.2 THE DISCRIMINANT

The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,. The discriminant allows you to determine the nature of the roots of the equation because discriminant

CASE #1 If, then is a real number and therefore there are distinct solutions. positive 2 real

CASE #2 If, then, so the two solutions from the quadratic formula are both. We call this a. double root

CASE #3 If, then D is negative and would be an number. So, there are distinct solutions. **Note: Imaginary solutions ALWAYS come in pairs – complex conjugates! imaginary 2

If the roots are real, we can also determine if the roots are rational or irrational. If D is a perfect square, the roots are rational. If D is not a perfect square, the roots are irrational.

Find the value of the discriminant and tell how may real and how many imaginary roots the equation has. If it has any real roots, tell whether they are rational. 1.

Find the value of the discriminant and tell how may real and how many imaginary roots the equation has. If it has any real roots, tell whether they are rational. 2.

Find the value of the discriminant and tell how may real and how many imaginary roots the equation has. If it has any real roots, tell whether they are rational. 3.

Find the value of the discriminant and tell how may real and how many imaginary roots the equation has. If it has any real roots, tell whether they are rational. 4.

Determine the value of k for which the given equation will have exactly one real root. 5.

Determine the value of k for which the given equation will have exactly one real root. 6.

Determine the value of k for which the given equation will have two distinct real roots. 7.