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(b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square?
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(b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, ...
Quadratic Polynomial with Zeros as (alpha + beta)^2 and (alpha - beta)^2
To find a quadratic polynomial with zeros as (alpha + beta)^2 and (alpha - beta)^2, we can use the fact that the sum and product of the zeros of a quadratic polynomial ax^2 + bx + c are related to its coefficients.
Finding the Sum and Product of Zeros:
Given that a and beta are the zeros of the quadratic polynomial x^2 - 3x + 2, we can find their sum and product using Vieta's formulas.
Sum of zeros, a + beta = -(-3) = 3
Product of zeros, a*beta = 2
Finding the New Zeros:
Let x = (alpha + beta)^2
=> x = (alpha^2 + 2alpha*beta + beta^2)
=> x = alpha^2 + beta^2 + 2alpha*beta
Let y = (alpha - beta)^2
=> y = (alpha^2 + beta^2 - 2alpha*beta)
Creating the Quadratic Polynomial:
Now, we can create a new quadratic polynomial with the given zeros.
The new polynomial will have the form x^2 - (sum of zeros)x + product of zeros
Substitute the values of the sum and product of zeros into the form:
New polynomial = x^2 - 3x + 2
Therefore, the quadratic polynomial with zeros as (alpha + beta)^2 and (alpha - beta)^2 is x^2 - 3x + 2.
To find a quadratic polynomial with zeros as (alpha + beta)^2 and (alpha - beta)^2, we can use the fact that the sum and product of the zeros of a quadratic polynomial ax^2 + bx + c are related to its coefficients.
Finding the Sum and Product of Zeros:
Given that a and beta are the zeros of the quadratic polynomial x^2 - 3x + 2, we can find their sum and product using Vieta's formulas.
Sum of zeros, a + beta = -(-3) = 3
Product of zeros, a*beta = 2
Finding the New Zeros:
Let x = (alpha + beta)^2
=> x = (alpha^2 + 2alpha*beta + beta^2)
=> x = alpha^2 + beta^2 + 2alpha*beta
Let y = (alpha - beta)^2
=> y = (alpha^2 + beta^2 - 2alpha*beta)
Creating the Quadratic Polynomial:
Now, we can create a new quadratic polynomial with the given zeros.
The new polynomial will have the form x^2 - (sum of zeros)x + product of zeros
Substitute the values of the sum and product of zeros into the form:
New polynomial = x^2 - 3x + 2
Therefore, the quadratic polynomial with zeros as (alpha + beta)^2 and (alpha - beta)^2 is x^2 - 3x + 2.
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(b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square?
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(b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about (b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square?.
(b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about (b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (b) If a and ẞ are the zeros of the quadratic polynomial x2 – 3x + 2, find a quadratic - polynomial whose zeros are aplha + beta whole square and alpha -beta whole square?.
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