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If alpha and beta are zeroes of polynomial f(x)= x^2-5x+4, find the value of 1/alpha +1/beta -2×alpha×beta

Posted by Anshika Pal 2 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Adithya Dev A 2 years, 11 months ago

f (x) = x^2 - 5x + 4 = 0. According to the relationship between zeroes and coefficients in quadratic equations, if α and β are the zeroes of f (x), then :- α + β = -b/a = 5.// αβ = c/a = 4.// Therefore, 1/α + 1/β - 2αβ = α + β/αβ - 2αβ = 5/4 - 2(4) = 5/4 - 8 = (5 - 32)/4 = -27/4 = -6.75.

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