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If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is?
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If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha b...
Solution:
Given quadratic equation is: x^2 - 4x + 1 = 0
To find the value of ααβ - αβ, we need to find the values of α and β first.
The sum of the zeros of a quadratic equation is given by the formula: α + β = -b/a
Here, the coefficient of x^2 is 1 and the coefficient of x is -4. So, substituting the values in the formula, we get:
α + β = -(-4)/1
= 4/1
= 4
The product of the zeros of a quadratic equation is given by the formula: αβ = c/a
Here, the constant term is 1 and the coefficient of x^2 is 1. So, substituting the values in the formula, we get:
αβ = 1/1
= 1
Hence, αβ = 1.
Now, let's calculate ααβ - αβ:
ααβ - αβ = α(α + β) - αβ
= α(4) - 1
= 4α - 1
Therefore, ααβ - αβ is equal to 4α - 1.
So, the final answer is 4α - 1.
Note: The values of α and β are not given in the question. To solve the quadratic equation and find the values of α and β, we can use the quadratic formula or factorization method.
Given quadratic equation is: x^2 - 4x + 1 = 0
To find the value of ααβ - αβ, we need to find the values of α and β first.
The sum of the zeros of a quadratic equation is given by the formula: α + β = -b/a
Here, the coefficient of x^2 is 1 and the coefficient of x is -4. So, substituting the values in the formula, we get:
α + β = -(-4)/1
= 4/1
= 4
The product of the zeros of a quadratic equation is given by the formula: αβ = c/a
Here, the constant term is 1 and the coefficient of x^2 is 1. So, substituting the values in the formula, we get:
αβ = 1/1
= 1
Hence, αβ = 1.
Now, let's calculate ααβ - αβ:
ααβ - αβ = α(α + β) - αβ
= α(4) - 1
= 4α - 1
Therefore, ααβ - αβ is equal to 4α - 1.
So, the final answer is 4α - 1.
Note: The values of α and β are not given in the question. To solve the quadratic equation and find the values of α and β, we can use the quadratic formula or factorization method.
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If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is? 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 alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is?.
If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is? 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 alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of x square - 4 x 1 then Alpha alpha beta minus alpha beta is?.
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