Question

Two real solutions of tx^2+3x_7=0

Answer 1

The number of solutions of a quadratic equation

ax^2+bx+c=0

Depends on its discriminant

/Delta=b^2-4ac

If /Delta>0 there are two distinct solutions

If /Delta=0 there are two coincident solutions

If /Delta<0 there are no solutions.

We know that there are two real solutions (I assume you mean distinct solutions), so we know that the discriminant is positive:

The number of solutions of a quadratic equation

Depends on its discriminant

If there are two distinct solutions

If there are two coincident solutions

If there are no solutions.

We know that there are two real solutions (I assume you mean distinct solutions), so we know that the discriminant is positive:

b^2-4ac=9+28t>0\iff t>-\dfrac[9][28]