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Relations between Roots and Coefficients : Higher Order Equations

12. If k is a...

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12. If k is any non zero constant and α,β are the zeroes of x+ax+1, then the polynomial whose zeroes are α/β and β/α is

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α

β

are the zeros of the polynomial

x^{2} + 4 x + 3

. The polynomial whose zeros are

1 + \frac{β}{α}

1 + \frac{α}{β}

α

β

are the zeroes of polynomial

P (x) = x^{2} - 3 x + 2 k

α + β = α . β

, then the value of k is ...............

α

β

x^{2} - 3 x - 2

then find quadratic polynomial whose zeros are

1) \frac{1}{2} α + β

\frac{1}{2} β + α

2) α - \frac{1}{α} + 1

β - \frac{1}{β} + 1

α a n d β

are the zeroes of the quadratic polynomial

2 S^{2} - 8 S + 4

, then the value of

\frac{α}{β} + \frac{β}{α} + 2 (\frac{1}{α} + \frac{1}{β}) + 3 α β

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Relations between Roots and Coefficients : Higher Order Equations

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