Statement-I: If a, b, c in R and the equation | vedclass

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Question

(D) For $x^2 + 3x + 4 = 0$,the discriminant $D = 3^2 - 4(1)(4) = 9 - 16 = -7 < 0$.Since $a, b, c \in R$,the complex roots must occur in conjugate pair

Vedclass · Accepted Answer

Statement-$I$ is false,Statement-$II$ is true.

Vedclass · Answer

(D) For $x^2 + 3x + 4 = 0$,the discriminant $D = 3^2 - 4(1)(4) = 9 - 16 = -7 Since $a, b, c \in R$,the complex roots must occur in conjugate pairs.If one root is common,both roots must be common.Thus,the coefficients must be proportional: $\frac{a}{1} = \frac{b}{3} = \frac{c}{4} = k$.Then,$\frac{a+c}{b} = \frac{k+4k}{3k} = \frac{5k}{3k} = \frac{5}{3}$.Since $\frac{5}{3} 
eq \frac{4}{3}$,Statement-$I$ is false.Statement-$II$ is a standard theorem for equations with both roots common,which is true.

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