Let f ( x ) = a x 2 + b x + c , g ( x ) = a x 2 + p x + q where a , b , c , q , p , ∈ R and b  = p . If their discriminants are equal and f ( x ) = g ( x ) has a root α , then

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a α 2 + b α + c = a α 2 + p α + q ⇒ α = b − p q − c ​ → ( i ) And b 2 − 4 a c = p 2 − 4 a q ⇒ b 2 − p 2 = 4 a ( c − q ) ​ ⇒ b + p = b − p 4 a ( c − q ) ​ = − 4 a α ​ ​ ( f ro m ( i )) α = 4 a − ( b + p ) ​ = 4 a − b ​ − a p ​ ​ w hi c h i s A . M o f a ll t h e roo t s o f f ( x ) = 0 an d g ( x ) = 0

Mathematics - Quadratic Equation Question with Solution | TestHub

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