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

Mar 31, 2018

$c < \frac{4}{3}$ or $c \in \left(- \infty , \frac{4}{3}\right)$

#### Explanation:

For an equation $a {x}^{2} + b x + c = 0$, we have two real roots if discriminant is greater than zero i.e. ${b}^{2} - 4 a c > 0$.

Here equation we have is

$3 {x}^{2} - 4 x + c = 0$ and hence the condition is

${\left(- 4\right)}^{2} - 4 \cdot 3 \cdot c = 16 - 12 c > 0$

or $12 c < 16$

i.e. $c < \frac{16}{12}$ i.e. $c < \frac{4}{3}$ or $c \in \left(- \infty , \frac{4}{3}\right)$