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If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.?
Most Upvoted Answer
If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4...
Given Information:
- Zeros of the quadratic polynomial f(x) are alpha and beta.
- f(x) = kx^2 + 4x + 4
- Sum of squares of zeros: (alpha)^2 + (beta)^2 = 24
Sum of Zeros:
- Sum of zeros (alpha + beta) = -b/a (using Vieta's formulas for a quadratic equation)
Product of Zeros:
- Product of zeros (alpha * beta) = c/a (using Vieta's formulas for a quadratic equation)
Using Sum and Product of Zeros:
- (alpha)^2 + (beta)^2 = (alpha + beta)^2 - 2(alpha * beta)
- 24 = (-4/k)^2 - 2(4/k)
Solving for k:
- 24 = 16/k^2 - 8/k
- Multiplying by k to clear the fraction: 24k = 16 - 8k
- 24k + 8k = 16
- 32k = 16
- k = 16/32
- k = 1/2
Conclusion:
Therefore, the value of k is 1/2 to satisfy the given condition that the sum of the squares of the zeros of the quadratic polynomial f(x) is 24.
- Zeros of the quadratic polynomial f(x) are alpha and beta.
- f(x) = kx^2 + 4x + 4
- Sum of squares of zeros: (alpha)^2 + (beta)^2 = 24
Sum of Zeros:
- Sum of zeros (alpha + beta) = -b/a (using Vieta's formulas for a quadratic equation)
Product of Zeros:
- Product of zeros (alpha * beta) = c/a (using Vieta's formulas for a quadratic equation)
Using Sum and Product of Zeros:
- (alpha)^2 + (beta)^2 = (alpha + beta)^2 - 2(alpha * beta)
- 24 = (-4/k)^2 - 2(4/k)
Solving for k:
- 24 = 16/k^2 - 8/k
- Multiplying by k to clear the fraction: 24k = 16 - 8k
- 24k + 8k = 16
- 32k = 16
- k = 16/32
- k = 1/2
Conclusion:
Therefore, the value of k is 1/2 to satisfy the given condition that the sum of the squares of the zeros of the quadratic polynomial f(x) is 24.
Community Answer
If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4...
K=-1 and 2/3
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If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.?
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If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.? 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 the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.? 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 the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.?.
If alpha and beta are the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.? 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 the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.? 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 the zeros of quadratic polynomial f(x)=kx^2+4x+4, such that (alpha)^2+(beta)^2=24, find the values of k.?.
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