Question

How do use the discriminant to find all values of c for which the equation `3x^2-4x+c=0` has two real roots?

Answer 1

`c<4/3` or `cin(-oo,4/3)`

Explanation:

For an equation `ax^2+bx+c=0`, we have two real roots if discriminant is greater than zero i.e. `b^2-4ac>0`.

Here equation we have is

`3x^2-4x+c=0` and hence the condition is

`(-4)^2-4*3*c=16-12c>0`

or `12c<16`

i.e. `c<16/12` i.e. `c<4/3` or `cin(-oo,4/3)`