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 [tex]a x^{2}+b x+c=0[/tex] solution of the equation is given by
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
The given equation is [tex]x^{2}+3 x+4=0[/tex] So in our case, a = 1, b = 3 and c = 4
On applying quadratic formula we get
[tex]\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}[/tex]
As i is square root of -1,
[tex]\Rightarrow x=-\frac{3}{2} \pm \frac{\sqrt{7}}{2} i[/tex]
Hence correct option is C that is roots of quadratic equation [tex]x^{2}+3 x+4=0 \text { are }-\frac{3}{2} \pm \frac{\sqrt{7}}{2} i[/tex]
