Question

find all solutions of the equation ${x}^{2} + 2x + 5 = 0$first input the solution with b < 0 here: the real number a equals ______and the real number b equals ______the input the solution with b > 0 here:the real number a equals ______and the real number b equals ______

Answer 1

Problem

Solution

For this case we cna use the quadratic formula given by:

$x=\frac{-b+\sqrt[]{b^2-4ac}}{2a}$

Where a= 1, b= 2, c=5. Replacing we got:

$x=\frac{-2-\sqrt[]{4-4(1)(5)}}{2(1)}=\frac{-2-\sqrt[]{-16}}{2}=-1-2i$$x=\frac{-2+\sqrt[]{4-4(1)(5)}}{2(1)}=\frac{-2+\sqrt[]{-16}}{2}=-1+2i$

And then the solution would be:

When b<0

a= -1

b= -2

When b>0

a= -1

b= 2