Product of real roots of equation $${t^2}{x^2} + \left| x \right| + 9 = 0$$
A
is always positive
B
is always negative
C
does not exist
D
none of these
Explanation
Product of real roots $$ = {9 \over {{t^2}}} > 0,\forall \,t\, \in R$$
$$\therefore$$ Product of real roots is always positive.
4
AIEEE 2002
MCQ (Single Correct Answer)
If $$\alpha \ne \beta $$ but $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3$$ then the equation having $$\alpha /\beta $$ and $$\beta /\alpha \,\,$$ as its roots is
A
$$3{x^2} - 19x + 3 = 0$$
B
$$3{x^2} + 19x - 3 = 0$$
C
$$3{x^2} - 19x - 3 = 0$$
D
$${x^2} - 5x + 3 = 0$$
Explanation
We have $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3;$$
$$ \Rightarrow \alpha \,\,\& \,\,\beta $$ are roots of