If alpha and beta are the roots of the equation (x-a)(x-b)-c=0, then find the roots of the equation (x-alpha)(x-beta)-c=0
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Step-by-step explanation:
(x-a)(x-b)-c = 0
x² - (a+b)x + ab - c = 0
∝+β = a+b
∝β = ab-c
as for the equation (x-alpha)(x-beta)-c=0
x² - (∝+β)x + ∝β - c = 0
x = { ∝+β ± √( (∝+β)² - 4(∝β-c))}÷2 = { a+b ± √( (a+b)² - 4(ab-2c))}÷2
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