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

Question

The point (t2+2 t+5,2 t2+t-2) lies on the line x+y=2 for (A) All real values of t (B) Some real values of t (C) t=(-3 ± √3/6) (D) None of these

Tardigrade Admin · Accepted Answer

The given point lies on the lines x+y=2, if 3 t2+3 t+3=0. Here discriminant 9-12 < 0. Therefore the value of t is imaginary. Thus the given point cannot lie on the line.

Q. The point $(t^{2} + 2 t + 5, 2 t^{2} + t - 2)$ lies on the line $x + y = 2$ for

All real values of $t$

Some real values of $t$

$t = \frac{- 3 \pm 3}{6}$

None of these

The given point lies on the lines $x + y = 2$ ,
if $3 t^{2} + 3 t + 3 = 0$ .
Here discriminant $9 - 12 < 0$ .
Therefore the value of $t$ is imaginary.
Thus the given point cannot lie on the line.

Q. The point (t2+2t+5,2t2+t−2) lies on the line x+y=2 for

All real values of t

Some real values of t

t=6−3±3​​