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If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial?
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Introduction:
In this problem, we are given a quadratic polynomial and we need to find a new quadratic polynomial whose zeros are half of the zeros of the given polynomial.
Given:
Polynomial x^2 - 7x + 10
Solution:
To find the zeros of the given polynomial, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values from the given polynomial, we get:
x = (7 ± √(7^2 - 4(1)(10))) / 2
x = (7 ± √9) / 2
x = 5 or 2
Therefore, the zeros of the given polynomial are 5 and 2.
To find the zeros of the new polynomial whose zeros are half of the given polynomial, we can simply divide the zeros of the given polynomial by 2:
5/2 and 2/2 = 1
Therefore, the zeros of the new polynomial are 5/2 and 1.
Now, we can use these zeros to form a new quadratic polynomial:
(x - 5/2)(x - 1) = x^2 - (5/2 + 1)x + (5/2)
Simplifying, we get:
x^2 - (7/2)x + (5/2)
Therefore, the new quadratic polynomial whose zeros are half of the zeros of the given polynomial is x^2 - (7/2)x + (5/2).
Conclusion:
We have found a new quadratic polynomial whose zeros are half of the zeros of the given polynomial by dividing the zeros of the given polynomial by 2 and using them to form a new polynomial. The final polynomial is x^2 - (7/2)x + (5/2).
In this problem, we are given a quadratic polynomial and we need to find a new quadratic polynomial whose zeros are half of the zeros of the given polynomial.
Given:
Polynomial x^2 - 7x + 10
Solution:
To find the zeros of the given polynomial, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values from the given polynomial, we get:
x = (7 ± √(7^2 - 4(1)(10))) / 2
x = (7 ± √9) / 2
x = 5 or 2
Therefore, the zeros of the given polynomial are 5 and 2.
To find the zeros of the new polynomial whose zeros are half of the given polynomial, we can simply divide the zeros of the given polynomial by 2:
5/2 and 2/2 = 1
Therefore, the zeros of the new polynomial are 5/2 and 1.
Now, we can use these zeros to form a new quadratic polynomial:
(x - 5/2)(x - 1) = x^2 - (5/2 + 1)x + (5/2)
Simplifying, we get:
x^2 - (7/2)x + (5/2)
Therefore, the new quadratic polynomial whose zeros are half of the zeros of the given polynomial is x^2 - (7/2)x + (5/2).
Conclusion:
We have found a new quadratic polynomial whose zeros are half of the zeros of the given polynomial by dividing the zeros of the given polynomial by 2 and using them to form a new polynomial. The final polynomial is x^2 - (7/2)x + (5/2).
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If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial?
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If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial? 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 If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial?.
If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial? 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 If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of polynomial x square -7x 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial?.
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