Math Problem Statement
let p,q,r be real numbers if px^2 + qx + r = 0 has two real roots α and β where α < -1 and β> 1 find value of 1 + r/p + |q/p|
Solution
We are given the quadratic equation:
with two real roots and , where and . We are asked to find the value of .
Step 1: Use Vieta's formulas
For a quadratic equation , Vieta's formulas tell us:
- The sum of the roots:
- The product of the roots:
Step 2: Use root information
Given that and , let's take specific values to simplify the calculations. Let’s choose and , which satisfy the condition and .
Using these values:
Step 3: Calculate the required expression
We need to find the value of: Substitute and :
Final Answer:
The value of is .
Would you like a deeper explanation or have any questions?
Here are 5 related questions to expand on this problem:
- How does Vieta's formulas help solve quadratic equations with real roots?
- What conditions guarantee that a quadratic equation has real roots?
- How do transformations affect the graph of a quadratic function?
- What happens when both roots of a quadratic equation are negative?
- How can we factor a quadratic equation with given roots?
Tip: When solving quadratic equations, always check if the discriminant is non-negative for real roots.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vieta's Formulas
Formulas
Sum of roots: α + β = -q/p
Product of roots: αβ = r/p
Quadratic equation: px^2 + qx + r = 0
Theorems
Vieta's Formulas
Suitable Grade Level
Grades 9-11
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