If the equations `x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0` have a common root, then it must be equal to a.`(p^(prime)-p ^(prime) q)/(q-q^(prime))` b. `(q-q ')/(p^(prime)-p)` c. `(p^(prime)-p)/(q-q^(prime))` d. `(p q^(prime)-p^(prime) q)/(p-p^(prime))`

Options

A. `(pq'- p'q)/(q-q')`
B. `(q-q')/(p'-p)`
C. `(p'=p)/(q-q')`
D. `(pq'- p'q)/(p-p')`

Answer

1,2

Explanation

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 ')`