| DIRECTION: Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following- |
| Statement-1: If\[a,\,\,b,\,\,c\]are noncomplex and\[\alpha ,\,\,\beta \] are the roots of the equation\[a{{x}^{2}}+bx+c=0\] then\[\operatorname{Im}(\alpha \beta )\ne 0\]. |
| Statement-2: A quadratic equation with non-real complex coefficient do not have root which are conjugate of other. |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: A
Solution :
\[i{{x}^{2}}+(1+i)x+i=0\] \[\Rightarrow \] \[\alpha \beta =1\] \[\Rightarrow \]\[\operatorname{Im}(\alpha \beta )=0\]
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