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If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.?
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If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - ...
Polynomial with zeroes 2a + 3ẞ and 3a + 2ẞ
Using Vieta's formulas:
To find the polynomial with zeroes 2a + 3ẞ and 3a + 2ẞ, we first need to consider the sum and product of these zeroes.
Let's consider the sum of the new zeroes:
(2a + 3ẞ) + (3a + 2ẞ) = 5a + 5ẞ
And the product of the new zeroes:
(2a + 3ẞ)(3a + 2ẞ) = 6a^2 + 4aẞ + 9aẞ + 6ẞ^2 = 6a^2 + 13aẞ + 6ẞ^2
Finding the sum and product of the new zeroes:
Now, using Vieta's formulas, we know that for a quadratic polynomial ax^2 + bx + c, the sum of the roots is given by -b/a and the product of the roots is given by c/a.
In our case, the sum of the new zeroes is 5a + 5ẞ and the product of the new zeroes is 6a^2 + 13aẞ + 6ẞ^2.
Forming the required polynomial:
The polynomial with the new zeroes can be expressed as:
x^2 - (sum of the new zeroes)x + product of the new zeroes
Substituting the values of the sum and product of the new zeroes, we get:
x^2 - (5a + 5ẞ)x + (6a^2 + 13aẞ + 6ẞ^2)
Therefore, the required polynomial with zeroes 2a + 3ẞ and 3a + 2ẞ is:
x^2 - (5a + 5ẞ)x + (6a^2 + 13aẞ + 6ẞ^2)
- Using Vieta's formulas
- Finding the sum and product of the new zeroes
- Forming the required polynomial
Using Vieta's formulas:
To find the polynomial with zeroes 2a + 3ẞ and 3a + 2ẞ, we first need to consider the sum and product of these zeroes.
Let's consider the sum of the new zeroes:
(2a + 3ẞ) + (3a + 2ẞ) = 5a + 5ẞ
And the product of the new zeroes:
(2a + 3ẞ)(3a + 2ẞ) = 6a^2 + 4aẞ + 9aẞ + 6ẞ^2 = 6a^2 + 13aẞ + 6ẞ^2
Finding the sum and product of the new zeroes:
Now, using Vieta's formulas, we know that for a quadratic polynomial ax^2 + bx + c, the sum of the roots is given by -b/a and the product of the roots is given by c/a.
In our case, the sum of the new zeroes is 5a + 5ẞ and the product of the new zeroes is 6a^2 + 13aẞ + 6ẞ^2.
Forming the required polynomial:
The polynomial with the new zeroes can be expressed as:
x^2 - (sum of the new zeroes)x + product of the new zeroes
Substituting the values of the sum and product of the new zeroes, we get:
x^2 - (5a + 5ẞ)x + (6a^2 + 13aẞ + 6ẞ^2)
Therefore, the required polynomial with zeroes 2a + 3ẞ and 3a + 2ẞ is:
x^2 - (5a + 5ẞ)x + (6a^2 + 13aẞ + 6ẞ^2)
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If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.?
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If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.?.
If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and ẞ are the zeroes of the quadratic polynomial f(x) = 2x ^ 2 - 5x + 7 find a polynomial whose zeroes are 2a + 3ẞ and 3a + 2β.?.
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