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Relations between Roots and Coefficients : Higher Order Equations

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Question

Find the values of k for which the zeroes of the polynomial f(n)=n^3 +12n^2+39n+k are in A.P

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Solution

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f (x) = x^{3} - 12 x^{2} + 39 x + k

k

α

β

2 y^{2} + 7 y + 5,

α + β + α β .

^{'} k^{'}, k - 3, 2 k + 1

4 k + 3

Find the value of k for which the polynomial x3-4x2+k has 3as it's zero

α

\frac{1}{α}

4 x^{2} - 2 x + k + 7

k

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