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Verify that −1+2i and −1− 2i are solutions to x²+2x+5=0.

User Haeminish
by
8.5k points

1 Answer

7 votes

Answer:NO

Explanation:

Given

Quadratic equation
x^2+2x+5=0

First we need to check discriminant of equation to know whether roots are real of imaginary


D=√(b^2-4ac)

here

a=1, b=2, c=5


D=√(2^2-4* 1* 5)


D=√(16-20)=√(-4)

thus D<0 therefore roots are imaginary

To verify given roots are roots of equation

sum of roots
=(-b)/(a)

Product of roots
=(c)/(a)


-1+2i-1-2i=(-2)/(1)

-2=-2

L.H.S=R.H.S

Product of roots


\left ( -1+2i\right )\left ( -1-2i\right )=1+2i-2i+2i^2


=1+2i^2=1-2=-1


L.H.S\\eq R.H.S


-1\\eq 5

thus given values are not solutions of given equation.

User Nzomkxia
by
8.9k points
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