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If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24?
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If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values...
Given Information:
- α, β are the roots of the quadratic polynomial kx^2 + 4x + 4.
- We need to find the values of k such that (α + β)^2 - 2αβ = 24.
Understanding the Problem:
- The sum of the roots of a quadratic equation is given by α + β = -b/a and the product of the roots is αβ = c/a, where the quadratic equation is of the form ax^2 + bx + c = 0.
- We are given that (α + β)^2 - 2αβ = 24, which can be simplified to α^2 + β^2 = 24.
Solution:
1. Using the sum and product of roots formula, we have:
- α + β = -4/k
- αβ = 4/k
2. We know that (α + β)^2 = α^2 + β^2 + 2αβ. Substituting the values:
- (-4/k)^2 = α^2 + β^2 + 2(4/k)
3. Simplifying the equation:
- 16/k^2 = 24 + 8/k
- 16 = 24k + 8
- 24k = -8
- k = -8/24
- k = -1/3
Conclusion:
- The value of k such that (α + β)^2 - 2αβ = 24 is k = -1/3.
- α, β are the roots of the quadratic polynomial kx^2 + 4x + 4.
- We need to find the values of k such that (α + β)^2 - 2αβ = 24.
Understanding the Problem:
- The sum of the roots of a quadratic equation is given by α + β = -b/a and the product of the roots is αβ = c/a, where the quadratic equation is of the form ax^2 + bx + c = 0.
- We are given that (α + β)^2 - 2αβ = 24, which can be simplified to α^2 + β^2 = 24.
Solution:
1. Using the sum and product of roots formula, we have:
- α + β = -4/k
- αβ = 4/k
2. We know that (α + β)^2 = α^2 + β^2 + 2αβ. Substituting the values:
- (-4/k)^2 = α^2 + β^2 + 2(4/k)
3. Simplifying the equation:
- 16/k^2 = 24 + 8/k
- 16 = 24k + 8
- 24k = -8
- k = -8/24
- k = -1/3
Conclusion:
- The value of k such that (α + β)^2 - 2αβ = 24 is k = -1/3.
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If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24?
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If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24?.
If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are zero of quadratic polynomial kx2 + 4x + 4, find the values of k such that (α + β)2 -2 αβ =24?.
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