Solve the equation $x^{2} + 3 x + 5 = 0$ for $x$ .

Open in App

Solution

The given quadratic equation is $x^{2} + 3 x + 5 = 0$

On comparing the given equation with ${a x}^{2} + b x + c = 0$ ,
we obtain $a = 1, b = 3,$ and $c = 5$
Therefore, the discriminant of the given equation is
$D = b^{2} - 4 a c = 3^{2} - 4 \times 1 \times 5 = 9 - 20 = - 11$
Therefore, the required solutions are
$x = \frac{- b \pm \sqrt{D}}{2 a} = \frac{- 3 \pm \sqrt{- 11}}{2 \times 1} = \frac{- 3 \pm \sqrt{11} i}{2}$

Suggest Corrections

Similar questions

Solve following equation for $x$ :
$x^{2} - 3 x - 10 = 0$

(x^{2} + \frac{1}{x^{2}}) - 3 (x - \frac{1}{x}) - 2 = 0

\frac{2 x - 3}{x^{2} - 2 x + 3} = \frac{3 x - 5}{x^{2} - 3 x + 5}

x

[0, 2]

1

0

(x^{2} + x + 1) + (x^{2} + 2 x + 3) + (x^{2} + 3 x + 5) + \dots \dots + (x^{2} + 20 x + 39) = 4500.

x^{2} - 3 x - 10 = 0

Join BYJU'S Learning Program