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Question

The nature of roots of the quadratic equation (xsinα)(xcosα)+3=0 are

A
Real and equal.
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B
Real and unequal.
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C
Imaginary.
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D
Rational and equal.
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Solution

The correct option is C Imaginary.
Given equation
x2(sinα+cosα)x+(sinα cosα+3)=0
For the nature of the roots
Δ=(sinα+cosα)24(sinα cosα+3)
=(sinαcosα)2430(sinαcosα)22
43Δ243
Δ is negative.

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