Q.

If the quadratic equations, x2+bx+c=0 and bx2+cx+1=0 have a common root then

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a

b + c + 1 = 0

b

b2+c2−1=bc−b−c

c

b + c - 1 = 0

d

b2+c2+1=bc+b+c

answer is A.

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Detailed Solution

Equations x2+bx+c=0 and bx2+cx+1=0 have a common root.(bc−1)2=c−b2b−c2⇒b2c2+1−2bc=bc−b3−c3+b2c2⇒1+c3+b3=3bc⇒(1+c+b)c2+b2+1−b−c−bc=0⇒b+c+1=0 and c2+b2+1=c+b+bc
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If the quadratic equations, x2+bx+c=0 and bx2+cx+1=0 have a common root then