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Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively?
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Find a quadratic polynomial each with the given number as the sum and ...
Quadratic Polynomial with Given Sum and Product of Zeroes
Introduction:
In this problem, we are given the sum and product of the zeroes of a quadratic polynomial and we need to find the polynomial. The general form of a quadratic polynomial is ax^2 + bx + c, where a, b, and c are constants.
Given Information:
- Sum of zeroes = S
- Product of zeroes = P
Formula:
- Sum of zeroes (S) = -b/a
- Product of zeroes (P) = c/a
Steps to Find the Quadratic Polynomial:
- Step 1: Use the formulas to create two equations
- Step 2: Substitute the given values of S and P into the equations
- Step 3: Solve the equations simultaneously to find the values of a, b, and c
- Step 4: Substitute the values of a, b, and c into the general form of the quadratic polynomial
Example:
Let's consider an example where the sum of zeroes is 5 and the product of zeroes is 6.
Given:
- Sum of zeroes (S) = 5
- Product of zeroes (P) = 6
Using the formulas:
- -b/a = 5
- c/a = 6
Solving the equations:
- From the first equation, we get b = -5a
- Substitute b = -5a into the second equation: -5a^2 = 6a
Solving for a, we get a = -3/5
Substitute a back into b = -5a, we get b = 3
Substitute a and b into the general form, we get the quadratic polynomial: -3/5x^2 + 3x + 6
Therefore, the quadratic polynomial with the sum of zeroes as 5 and the product of zeroes as 6 is -3/5x^2 + 3x + 6.
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Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively?
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Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively?.
Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively?.
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