Question

What is the solution to the following equation? x^2+3x+4=0

Answer 1

Answer:

x =−3±i√7/2

is the correc anwer

Answer 2

Option C

The solution of equation x^2+3x+4=0 is x= -3+- square root of -7/ 2

Solution:

Need to identify correct option for solution of the equation x^2 + 3x + 4 = 0.

Given equation is quadratic equation. We can find solution of this equation using quadratic formula.

According to quadratic formula for general equation $a x^{2}+b x+c=0$ solution of the equation is given by  

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

The given equation is $x^{2}+3 x+4=0$ So in our case, a = 1, b = 3 and c = 4

On applying quadratic formula we get

$\begin{array}{l}{x=\frac{-3 \pm \sqrt{3^{2}-4 \times 1 \times 4}}{2 \times 1}} \\\\ {x=\frac{-3 \pm \sqrt{9-16}}{2}} \\\\ {x=\frac{-3 \pm \sqrt{-7}}{2}} \\\\ {x=-\frac{3}{2} \pm \frac{(\sqrt{-1} \times \sqrt{7})}{2}}\end{array}$

As i is square root of -1,

$\Rightarrow x=-\frac{3}{2} \pm \frac{\sqrt{7}}{2} i$

Hence correct option is C that is roots of quadratic equation $x^{2}+3 x+4=0 \text { are }-\frac{3}{2} \pm \frac{\sqrt{7}}{2} i$