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If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta?
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If alpha and beta are the zeros of the polynomials p by x is equal to ...
Calculation of 1/Alpha and 1/Beta
There are two important relationships between the zeros of a polynomial and its coefficients. One of them is that the sum of the zeros of a polynomial is equal to the negative of the coefficient of the linear term divided by the coefficient of the quadratic term. The other relationship states that the product of the zeros of a polynomial is equal to the constant term divided by the coefficient of the quadratic term.
Finding the Zeros Alpha and Beta
Given that the polynomial is p(x) = 2x^2 + 3x + 5, we can find the zeros by setting p(x) equal to zero and solving for x. By using the quadratic formula, we get:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values a=2, b=3, and c=5 into the formula, we find that the zeros are:
Alpha = (-3 + sqrt(3^2 - 4*2*5)) / 4 = (-3 + sqrt(-31)) / 4
Beta = (-3 - sqrt(3^2 - 4*2*5)) / 4 = (-3 - sqrt(-31)) / 4
Calculating 1/Alpha and 1/Beta
To find 1/Alpha and 1/Beta, we simply take the reciprocal of the zeros:
1/Alpha = 1 / ((-3 + sqrt(-31)) / 4) = 4 / (-3 + sqrt(-31))
1/Beta = 1 / ((-3 - sqrt(-31)) / 4) = 4 / (-3 - sqrt(-31))
Therefore, the values of 1/Alpha and 1/Beta are 4 / (-3 + sqrt(-31)) and 4 / (-3 - sqrt(-31)) respectively.
There are two important relationships between the zeros of a polynomial and its coefficients. One of them is that the sum of the zeros of a polynomial is equal to the negative of the coefficient of the linear term divided by the coefficient of the quadratic term. The other relationship states that the product of the zeros of a polynomial is equal to the constant term divided by the coefficient of the quadratic term.
Finding the Zeros Alpha and Beta
Given that the polynomial is p(x) = 2x^2 + 3x + 5, we can find the zeros by setting p(x) equal to zero and solving for x. By using the quadratic formula, we get:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values a=2, b=3, and c=5 into the formula, we find that the zeros are:
Alpha = (-3 + sqrt(3^2 - 4*2*5)) / 4 = (-3 + sqrt(-31)) / 4
Beta = (-3 - sqrt(3^2 - 4*2*5)) / 4 = (-3 - sqrt(-31)) / 4
Calculating 1/Alpha and 1/Beta
To find 1/Alpha and 1/Beta, we simply take the reciprocal of the zeros:
1/Alpha = 1 / ((-3 + sqrt(-31)) / 4) = 4 / (-3 + sqrt(-31))
1/Beta = 1 / ((-3 - sqrt(-31)) / 4) = 4 / (-3 - sqrt(-31))
Therefore, the values of 1/Alpha and 1/Beta are 4 / (-3 + sqrt(-31)) and 4 / (-3 - sqrt(-31)) respectively.
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If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta?
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If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta?.
If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeros of the polynomials p by x is equal to 2x square + 3x + 5 find the value of 1 by Alpha and one by beta?.
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