Question

Assertion :Equation $i{x}^2+(i-1)x-\left(1/2\right)-i=0$ has imaginary roots. Reason: if $a=i,b=i-1\text{and}c=-\left(1/2\right)-i$, then $b^2-4ac<0$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$i{x}^2+(i-1)x-\frac{1}{2}-i=0$

$x=\frac{-(i-1)\pm \sqrt{(i-1{)}^2-4(i)(-\frac{i}{2}-i)}}{2i}=\frac{-(i-1)\pm \sqrt{-4}}{2i}$

Thus, roots are imaginary. Also, we have $b^2-4ac=-4<0,$ but this is not the correct reason for which roots are imaginary as coefficients of the equation are imaginary.

Hence, both the statements are correct but statement 2 is not correct explanation of statement 1