To state: If two quadratic equations share a solution if so, give two quadratic equation that meet the criterion. If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0.
Yes, two quadratic equations can share a solution. The equations are
Given information:
The given statement says to give two quadratic equations that share a solution.
Explanation:
Yes, two quadratic equations can share a solution.
Consider the below given examples:
Equation:
Compare this equation with
Its discriminate is:
The roots of a quadratic equation in the form
Substitute the values
Therefore, the discriminate with zero has one real solution for the equation
Now consider one more equation:
Compare this equation with
Its discriminate is:
The roots of a quadratic equation in the form
Substitute the values
Therefore, the discriminate with positive has two real solution for the equation
The equations can share common factors such as for
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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