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If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k?
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If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1...
Explanation:
Given that the polynomial is x² - 5x + k and α - β = 1.
Let's find the sum and product of the roots of the polynomial.
Sum of the roots:
α + β = 5/1 (By comparing the coefficients with ax² + bx + c = 0)
α + β = 5
Product of the roots:
αβ = k/1 (By comparing the constant terms with ax² + bx + c = 0)
αβ = k
Given that α - β = 1
Adding and subtracting equations (1) and (2), we get
α + β = 5
α - β = 1
Adding these two equations, we get
2α = 6
α = 3
Substituting α = 3 in equation (1), we get
β = 2
Value of k:
Substituting α and β in equation (2), we get
αβ = k
3 × 2 = k
k = 6
Therefore, the value of k is 6.
Given that the polynomial is x² - 5x + k and α - β = 1.
Let's find the sum and product of the roots of the polynomial.
Sum of the roots:
α + β = 5/1 (By comparing the coefficients with ax² + bx + c = 0)
α + β = 5
Product of the roots:
αβ = k/1 (By comparing the constant terms with ax² + bx + c = 0)
αβ = k
Given that α - β = 1
Adding and subtracting equations (1) and (2), we get
α + β = 5
α - β = 1
Adding these two equations, we get
2α = 6
α = 3
Substituting α = 3 in equation (1), we get
β = 2
Value of k:
Substituting α and β in equation (2), we get
αβ = k
3 × 2 = k
k = 6
Therefore, the value of k is 6.
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If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k?
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If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k? 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 α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k?.
If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k? 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 α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the zeros of polynomial x2 - 5x k such that α - β = 1. find the value of k?.
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