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If the equation x^2+px+q=0 and x^2+p'x+q...

If the equation `x^2+px+q=0` and `x^2+p'x+q'=0` have a common root show that it must be equal to `(pq'-p'q)/(q-q')` or `(q-q')/(p'-p)`

A

`(pq'- p'q)/(q-q')`

B

`(q-q')/(p'-p)`

C

`(p'=p)/(q-q')`

D

`(pq'- p'q)/(p-p')`

Text Solution

Verified by Experts

The correct Answer is:
1,2
Equation `x^(2) + px + q = 0 and x^(2) P 'x + q' = 0 ` have a common
root. Therefore .
` (q - q')^(2) = (pq'- p'q)(p'-p)` (1)
Subtracting two equation, we have
` x = (q - q')/(p'-p)`
Also using (1),
` x = (q-q')/(p'-p) = (pq' - p,q)/(q - q ')`
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