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If alpha and beta are the zeros of the polynomial x^2 - 6x + k. find the value of k such that [ alpha plus beta ]^2 - 2alpha beta = 40?
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If alpha and beta are the zeros of the polynomial x^2 - 6x + k. find t...
Given Information:
- Zeros of the polynomial: alpha, beta
- Polynomial: x^2 - 6x + k
- Expression to find: [alpha + beta]^2 - 2alpha beta = 40

Explanation:

Finding the Sum and Product of Zeros:
- Sum of zeros (alpha + beta) = -(-6) = 6
- Product of zeros (alpha * beta) = k

Using Vieta's Formulas:
- [alpha + beta]^2 - 2alpha beta = 40
- Substituting values: (6)^2 - 2k = 40
- Solving the equation: 36 - 2k = 40
- Simplifying further: 2k = -4
- Finding the value of k: k = -2

Final Answer:
- The value of k such that [alpha + beta]^2 - 2alpha beta = 40 is k = -2.
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If alpha and beta are the zeros of the polynomial x^2 - 6x + k. find the value of k such that [ alpha plus beta ]^2 - 2alpha beta = 40?
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