| Statement 1: If \[a,\,b,\,c\in R\] and the quadratic equation \[a{{x}^{2}}+bx+c=0\] and \[{{x}^{2}}+2x+3=0\] have a common root, \[a:b:c=1:2:3\]. |
| Statement 2: If \[a,\,b,\,c\in R\] and if one root is common then both the roots are common. |
A) Both statements are true, and Statement-2 explains Statement-1.
B) Both statements are true, but Statement-2 does not explain Statement-1.
C) Statement-1 is True, Statement-2 is False.
D) Statement-1 is False, Statement-2 is true.
Correct Answer: C
Solution :
\[\therefore \,\,{{x}^{2}}+2x+3=0\] has discriminant \[4-4\times 1\times 3<0\] \[\Rightarrow \] complex roots. \[\therefore \] both roots common. \[\therefore \,\,\frac{a}{1}=\frac{b}{2}=\frac{c}{3}\] \[\Rightarrow \,\,a:b:c=1:2:3\].
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