1) The document discusses using the discriminant to determine if quadratic equations have real or rational roots. 2) It provides examples of finding the values of a and b that give real roots, and finding the maximum value of y/x given real values of x and y that satisfy a quadratic equation. 3) It proves statements about quadratic equations with integer coefficients having rational or integer roots depending on the values of a, b, and c.

1. Application of Discriminant Some Interesting Examples

2. Discriminant& Real Roots Given that has no real roots, where m is a real number, show that the equation below in x has no real roots, either.

3. Given the equation has real roots. Find the value of a and b. Discriminantand Expression Value

4. Discriminantand Expression Value are all the real solution pairs satisfying the equation Hence, what is the maximum value of y/x?

5. Real x and y satisfy Find the extreme value of y. Discriminantand Expression Value

6. Given that m is a rational number. Find the value of k, such that equation below has rational roots. Discriminantand (ir)Rational / Integer Roots

7. Given a quadratic equation, has integer coefficients a, b and c. Prove: 1. If a, b and c are all odd numbers, the equation has no rational roots. 2. If a and b are even numbers and c is odd, the equation has no integer roots. Discriminantand (ir)Rational / Integer Roots

8. Given a quadratic equation, has real roots with p and q being odd. Prove that these two real roots must be irrational. Discriminantand (ir)Rational / Integer Roots