Question

x^2+x+5=0 by formula method​

Answer 1

The answer is

$\frac{ - 1±</p><p> i \sqrt{19} }{2}$

Explanation:

The quadratic formula is

$x = \frac{ - b ±</p><p>\sqrt{ {b}^{2} } - 4ac}{2a}$

For the equation

${ax}^{2} + bx + c$

In this case,

a=1 , b=1 , and c=5

You can therefore substitute in those values to get:

$\frac{ - 1± \sqrt{ {1}^{2} - 4(1)(5) } }{2(1)} </p><p>$

Simplify to get

$\frac{ - 1 ± \sqrt{ - 19} }{2}$

Because,

$\sqrt{ - 19}$

Is not a real number, we have to stick to imaginary solutions. (If this problem asks for real number solutions, there are none.)

The imaginary number ( i )equals

$\sqrt{ - 1}$

, Therefore we can substitute it in:

$\frac{ - 1 ± \sqrt{ -1. 19} }{2}$

$\frac{ - 1 ± \sqrt{ - 1} \sqrt{ 19} }{2}$

$\frac{ - 1 ± \: i \sqrt{ 19} }{2}$

The final answer.

Hope this helps!