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If alpha and bita are roots of equation, (x-a)(x-b) +c=0 find the roots of the equation (x-alpha)(x-bita)=c

If alpha and bita are roots of equation, (x-a)(x-b) +c=0 find the roots of the equation (x-alpha)(x-bita)=c

Grade:11

1 Answers

Ritesh Khatri
76 Points
6 years ago
(x –  \alpha)(x –  \beta)=c
x2 – (\alpha + \beta)x +\alpha \beta = c (eqn 1 )
 
also
 (x-a)(x-b) +c=0
x2 – (a+b)x +ab + c = 0
\alpha +\beta =a+b
\alpha\beta = ab + c
now eqn 1 becomes
 
x2 – (a+b)x + ab + c = c
x2 – (a+b)x + ab  = 0
and roots of this equation are a and b

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