Answer:
4x^2 + 100 = 0
x²+1=0
Step-by-step explanation:
Let's analyze each function:
1)
[tex]4x^2=100[/tex]
We can rewrite it as
[tex]4x^2=-100[/tex]
Or
[tex]x^2=-\frac{100}{4}=-25[/tex]
The term on the left, [tex]x^2[/tex], is the square of a number, therefore it cannot be negative: so, this equation has no real solutions.
2)
[tex]3x^2-9=0[/tex]
We can rewrite it as
[tex]3x^2=9[/tex]
Or
[tex]x^2=\frac{9}{3}=3[/tex]
Which has two real solutions:
[tex]x=\pm \sqrt{3}[/tex]
3)
[tex]x^2+1=0[/tex]
This can be rewritten as
[tex]x^2=-1[/tex]
The term on the left, [tex]x^2[/tex], is the square of a value: therefore, it cannot be negative. So, this equation has no real solutions.
