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Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other?
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Condition for Zeros of a Polynomial to be Reciprocal of Each Other
Given a quadratic polynomial: \( ax^2 + bx + c \)
Definition of Reciprocal Zeros
- Reciprocal zeros: Zeros that are the multiplicative inverse of each other
- Let the zeros be: \( \frac{1}{p} \) and \( \frac{1}{q} \)
Sum and Product of Zeros
- Sum of zeros: \( \frac{1}{p} + \frac{1}{q} = \frac{p + q}{pq} = -\frac{b}{a} \)
- Product of zeros: \( \frac{1}{p} \cdot \frac{1}{q} = \frac{1}{pq} = \frac{c}{a} \)
Condition for Reciprocal Zeros
- Equating the sum and product: \( \frac{p + q}{pq} = \frac{1}{pq} = -\frac{b}{a} = \frac{c}{a} \)
- Solving the equation: \( p + q = -b \) and \( pq = c \)
- Thus, the condition for the zeros to be reciprocal is: \( p + q = -b \) and \( pq = c \)
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Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other?
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Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other?.
Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the condition that zeros of polynomial a x square + bx + c are reciprocal of each other?.
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