Question

If x2 + px + q = 0 and x2 + qx + p = 0 have a common root, then

Answer 1

Dear Student,

Let common root be m

subtracting the two equations we ge that x = (q - q’)/(p’ - p)

Multiply eq 1 with q' and eq 2 with q

Subtract 2 from 1 to get

M= (p'q-pq') / (q'- q).

Answer 2

p = q

q + p + 1 = 0

p - q = 0

Step-by-step explanation:

Let the common root be a

so,

a^2 + pa + q = 0  ...(i)

and a^2 + qa + p = 0  ...(ii)

by solving (i) and (ii), we get

a^2/(p^2 - q^2) = a/q-p = 1/q-p

∵ a = (p^2 - q^2)/(q - p) and a = 1

⇒ (p^2 - q^2)/q - p = 1

⇒ p^2 - q^2 = q - p

or (p^2 - q^2) + (p - q) = 0

⇒ (p - q) (p + q + 1) = 0

⇒ p - q = 0

or

p + q + 1 = 0

Learn more: Common root

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