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Exercise 3. Number of solutions for Quadratic equations. The discriminant is the part of the quadratic formula under the square root. The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions.

Exercise 4. How many solutions roots does the following quadratic equation have? The discriminant should be more than 0. A discriminant of zero indicates that the quadratic has a repeated real number solution. Exercise 5. Find the value of k for the following quadratic equation, so that it has two equal roots. Solution: We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero.

A negative discriminant indicates that neither of the solutions are real numbers. Exercise 6. In order not to have real solution, discriminant should be less than 0. So, in the interval -9; 3 the quadratic equation above does not have real solution. Exercise 7. To solve rational equation: 1. Irrational Equations Any equation where the variable is inside a radical is called an irrational equation. When solving an irrational equation, the key step will be removing the radical.

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