The equation tx^2+3x-7=0 has two real solutions. what can dedused about the value of t?

if it has two real repeated solutions then t=-9/8

if it has two real distinct solutions then t>-9/28

Step-by-step explanation:

Given:

tx^2+3x-7=0

Also above equation has two real solutions

Now what can deduced about the value of t?

For any quadratic equation "ax^2 +bx +c=0" the solution is given by the quadratic formula

x=

The part under the square root i.e b^2 - 4ac is called the discriminant and it decides whether the equation will have 1 solution, 2 solution or no solution.

if discriminant is negative, i.e. <0 then equation will have no real solution

if discriminant is zero, i.e. =0 then equation will have two repeated real solution

if discriminant is positive, i.e >0 then equation will have two real distinct solution

As given equation has two real solutions:

if they are distinct then

b^2-4ac>0

Putting values of a=t, b=3, c=-7 in above we get,

9+28t>0

28t>-9

t>-9/28

if they are repeated then

b^2-4ac=0

Putting values of a=t, b=3, c=-7 in above we get,

9+28t=0

28t=-9

t=-9/28!