Question

If alpha and beta are the zeroes of the polynomial x^2+px+q, find the value of (alpha/beta + 2)(beta/alpha + 2)
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Answer 1

Answer:

5 - 2(p/q)

Step-by-step explanation:

alpha + beta = -p -----------(1)

(alpha)(beta) = q  --------------(2)

(alpha + beta)/(alpha)(beta) = -p/q  --------- (3)

Simplifying the given expression

(alpha/beta + 2)(beta/alpha + 2)

= alpha/beta*beta/alpha + 2*alpha/beta + 2*beta/alpha +4

=1+ 2*alpha/beta + 2*beta/alpha + 4    

= 5  + 2(alpha + beta)/(alpha)(beta)

= 5 +2 (-p/q)  (From (3) )

= 5 - 2(p/q)

Answer 2

Answer:

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