To Explain: Whether if two discriminants are equal, the solutions to the two equations are same. Explain the error and give an example of two quadratic equations.
No, if two discriminants are equal, the solutions to the two equations are not same.
Given:
If whether two discriminants are equal, the solutions to the two equations are same. Explain the error and give an example of two quadratic equations.
Explanation:
When there is one solution to an equation, the discriminants are all zero and thus equal, but if there are two or more solutions, they may or may not be equal.
For example,
Compared it with
Thus, the values are
The discriminate of the equation (1) is:
The roots of
Substitute
There is only one real solution for the discriminate with zero.
Consider another example:
Compared the above equation with
Thus, the values are
The discriminate of the equation is:
The roots of quadratic equation
Substitute
There is only one real solution for the discriminate with zero.
There is a discriminate zero in equations
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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