Discriminant and nature of the root.pptx

a lesson in grade 9 first quarter on discriminant and nature of the roots of a quadratic equations

1. Nature and Number of the Roots of a Quadratic Equation

2. Objectives: a. define discriminant, b. characterizes the roots of a quadratic equation using the discriminant, and c. answer the given activity.

3. Known as the discriminant  

4. If , where and are real numbers, then the discriminant D is .The word discriminant came from latin word “discrimen” which mean to distinguish. Discriminant is to distinguish the nature of the roots of a quadratic equation.  

5. Quadratic Equations with Real Coefficients If the discriminant is Positive and Not a Perfect Square the character of the roots is Real, Irrational, and Unequal. If the discriminant is Positive and a Perfect Square the character of the roots is Real, Rational, and Unequal.

6. Quadratic Equations with Real Coefficients 3. If the discriminant is Zero the character of the roots is Real, Rational and Equal. 4. If the discriminant is Negative the character of the roots is Imaginary and Unequal.

7. Nature of the Roots Positive and Not a Perfect Square Real, Irrational, and Unequal. Positive and a Perfect Square Real, Rational, and Unequal. Zero Real, Rational and Equal Negative Imaginary and Unequal. Nature of the Roots Positive and Not a Perfect Square Real, Irrational, and Unequal. Positive and a Perfect Square Real, Rational, and Unequal. Zero Real, Rational and Equal Negative Imaginary and Unequal.

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16. Assignment #1(Answer on your notebook) 1.     3.