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Question

The point t2+2t+5,2t2+t-2 lies on the line x+y=2 for


A

All real values of t

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B

Some real values of t

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C

t=-3±36

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D

No real values of t

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Solution

The correct option is D

No real values of t


Explanation for the correct answer:

Solve the given equation of line based on given information

In the question, it is given that point t2+2t+5,2t2+t-2 lies on the line x+y=2.

So, the point satisfies the given line, such that, x=t2+2t+5,y=2t2+t-2,

t2+2t+5+2t2+t-2=23t2+3t+3=23t2+3t+1=0

We know that the discriminant of the above quadratic equation is given by, D=b2-4ac

So,

D=32-4(3)(1)D=9-12<0

Therefore, there is no real value of t for which the given point will lie on the given line.

Hence, option D is the correct answer.


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