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Question

Given that q2pr<0,p>0, then the value of ∣ ∣pqpx+qyqrqx+rypx+qyqx+ry0∣ ∣ is

A
zero
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B
positive
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C
negative
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D
q2+pr
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Solution

The correct option is A negative
Δ=∣ ∣pqpx+qyqrqx+rypx+qyqx+ry0∣ ∣
Applying R3R3xR1yR2
Δ=∣ ∣ ∣pqpx+qyqrqx+ry00((px+qy)+(qx+ry))∣ ∣ ∣=((px+qy)+(qx+ry))(prq2)=(q2pr)((px+qy)+(qx+ry))
As q2pr<0
Δ<0

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