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

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
$b^{2} - 4 a c$
$(i - 1)^{2} + 4 i (\frac{3}{2})$
$= - 2 i + 6 i$
$= 4 i$
Since $b^{2} - 4 a c$ is imaginary, hence, the roots are imaginary.
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Hence, option 'B' is correct.

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Assertion :Equation ix2+(i−1)x−(1/2)−i=0 has imaginary roots. Reason: If a=i,b=i−1 and c=−(1/2)−i, then b2−4ac<0

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