# How do you find value of discriminant then describe number and type of solutions for 4x^2 - 4x +17 = 0?

Jan 19, 2016

$\Delta < 0$

${x}_{1 , 2} \in \mathbb{C}$

#### Explanation:

given:

$y = a {x}^{2} + b x + c = 0$

$\Delta = {b}^{2} - 4 a c$

$a = 4$
$b = - 4$
$c = 17$

$\therefore \Delta = 16 - 4 \cdot 4 \cdot 17 = 16 \left(1 - 17\right) = 16 \cdot \left(- 16\right) = - 256$

Then:

$\Delta < 0$

$\therefore {x}_{1 , 2} \in \mathbb{C}$