Question

tx^2+3x-7=0 has two real solutions . what can b deduced about value of t ?​

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:

$b^2-4ac = 9+28t > 0 \iff t>-\dfrac{9}{28}$