Respuesta :
Answer:
The given equation will have two roots as +5i and -5i
Step-by-step explanation:
Shasta claimed that the equation x^2+25=0 can be solved by using its factored form of (x+5i)^2=0, and that -5i is the only zero for this function
The given equation is [tex]x^2+25 =0[/tex]
This clearly shows it will have complex roots, and since it is a quadratic equation it will have 2 complex roots
[tex]x^2 = -25 \\x = \sqrt{-25} \\x= \sqrt{-1}* \sqrt{25}\\[/tex]
[tex]x = i\sqrt{25}[/tex]
x = ± 5i
It will be false to say that -5i will be the only complex root to this equation.
The given equation will have +5i and -5i as its roots.
Lets verify
x = +5i
[tex](5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25\\-25 + 25 = 0[/tex]
x = -5i
[tex](-5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25 \\-25 + 25 \\ = 0[/tex]
