Respuesta :
Answer:
The roots of the equation is: [tex]x=\pm i\frac{\sqrt{7}}{7}[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]7x^2+1=0[/tex]
Subtract 1 from both the sides.
[tex]7x^2+1-1=-1[/tex]
[tex]7x^2=-1[/tex]
Isolate the variable by dividing both the side by 7.
[tex]\frac{7x^2}{7}=\frac{-1}{7}[/tex]
[tex]x^2=\frac{-1}{7}[/tex]
Take the square root:
[tex]x=\pm \sqrt{\frac{-1}{7}}[/tex]
[tex]x=\pm \frac{1}{\sqrt{7}}i[/tex]
Now we multiply the numerator and the denominator by √7:
[tex]x=\pm \frac{1}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}i[/tex]
[tex]x=\pm \frac{\sqrt{7}}{7}i[/tex]
[tex]x=\pm i\frac{\sqrt{7}}{7}[/tex]
Hence, the roots of the equation is: [tex]x=\pm i\frac{\sqrt{7}}{7}[/tex]
