Application of discriminant
0 likes413 views
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.
Application of discriminant
- 1. Application of DiscriminantSome Interesting Examples
- 2. Discriminant& Real RootsGiven 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