if alpha and beta are the zeroes of the polynomial 6y^2 (six y squared) - 7y + 2, find a quadratic polynomial whose zeroes are 1/alpha + 1/beta

Question

Mathematics

Dane Kirk

24 January, 06:04

if alpha and beta are the zeroes of the polynomial 6y^2 (six y squared) - 7y + 2, find a quadratic polynomial whose zeroes are 1/alpha + 1/beta

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Answers (1)

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Janiah Perry · Answer 1

6y² - 7y + 2 = 0

y=7±√ (49-4*6*2) / 12

= 7±1 / 12

= ½ or ⅔

so we want our polynomial to have roots of 2 and 3/2

(x-2) (x-3/2) = 0

x² - 7/2x + 3 = 0