Answer:NO
Step-by-step explanation:
Given
Quadratic equation [tex]x^2+2x+5=0[/tex]
First we need to check discriminant of equation to know whether roots are real of imaginary
[tex]D=\sqrt{b^2-4ac}[/tex]
here
a=1, b=2, c=5
[tex]D=\sqrt{2^2-4\times 1\times 5}[/tex]
[tex]D=\sqrt{16-20}=\sqrt{-4}[/tex]
thus D<0 therefore roots are imaginary
To verify given roots are roots of equation
sum of roots[tex]=\frac{-b}{a}[/tex]
Product of roots[tex]=\frac{c}{a}[/tex]
[tex]-1+2i-1-2i=\frac{-2}{1}[/tex]
-2=-2
L.H.S=R.H.S
Product of roots
[tex]\left ( -1+2i\right )\left ( -1-2i\right )=1+2i-2i+2i^2[/tex]
[tex]=1+2i^2=1-2=-1[/tex]
[tex]L.H.S\neq R.H.S[/tex]
[tex]-1\neq 5[/tex]
thus given values are not solutions of given equation.
