# How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given x^2+4x+3=0?

Mar 6, 2017

$\Delta = 16 - 12 = 4 > 0$

$: . \text{the quadratic has two unequal real roots} .$

$x = - 1 , - 3$

#### Explanation:

$\text{For the quadratic equation } a {x}^{2} + b x + c = 0$

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

$\Delta > 0 \implies \text{two unequal real roots}$

$\Delta = 0 \implies \text{two equal roots}$

$\Delta < 0 \implies \text{ complex roots }$

${x}^{2} + 4 x + 3 = 0$

$a = 1 , b = 4 , c = 3$

$\Delta = {4}^{2} - 4 \times 1 \times 3$

$\Delta = 16 - 12 = 4 > 0$

$: . \text{the quadratic has two unequal real roots} .$

solving with formula

${x}^{2} + 4 x + 3 = 0$

$x = \frac{- b \pm \sqrt{\Delta}}{2 a}$

$x = \frac{- 4 \pm \sqrt{4}}{2}$

$x = \frac{- 4 \pm 2}{2}$

${x}_{1} = \frac{- 4 + 2}{2} = - 1$

${x}_{2} = \frac{- 4 - 2}{2} = - 3$