Math Problem Statement
Solution
To find the equation that has roots of and , we need to remember that for a quadratic equation, the factors are based on the roots as follows:
If the roots are and , the equation can be written as:
Given the roots and :
- Substitute and .
- This gives us the factors and .
- So, the equation should be:
Answer: The correct option is A: .
Would you like further details or have any questions?
Here are some related questions:
- How do you find the roots of a quadratic equation given in standard form?
- What would be the equation if the roots were and ?
- How can you expand to write the equation in standard form?
- What is the relationship between the coefficients and the roots of a quadratic equation?
- How do we verify that and satisfy the equation ?
Tip: Remember that the roots of an equation are the values of that make each factor equal to zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Roots of Equations
Formulas
(x - r1)(x - r2) = 0 for roots r1 and r2
Theorems
Root-Factor Relationship in Quadratic Equations
Suitable Grade Level
Grades 8-10
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