Math Problem Statement
The roots of the quadratic equation ax^2 + bx + c = 0 are α and β and the roots of the equation a'x^2 + b'x + c = 0 are α' and -β. Show that the square equation x^2\ (b/a)+(b'/a') + x + 1\ (b/c)+(b'/c') = 0 with α and α' as roots.
Solution
To prove that the quadratic equation has roots and , we will follow these steps:
Step 1: Write the given quadratic equations with their roots
Given:
- The quadratic equation has roots and .
- The quadratic equation has roots and .
Using Vieta's formulas for the roots:
-
For :
-
For ( a'x^2
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Vieta's Formulas
Formulas
Quadratic equation ax^2 + bx + c = 0
Vieta's formulas for quadratic roots
Theorems
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Suitable Grade Level
Grades 10-12
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