Roots of the equation 7x²+1=0:
7x²+1=0, now we transfer 1 to the right:
7x²=-1, divide by 7:
x²=-1/7, take the square root:
x=+/-√(-1/7)=+/-(i/√7), now we multiply the numerator and the denominator by √7, and we see that we have two complex roots:
x=+/-(i√7)/(√7*√7)=+/-(i√7)/7
We have two possible roots:
x₁=+(i√7)/7 and x₂=-(i√7)/7, so the correct answer is the last one on the image:
x₁,₂=+/-(i√7)/7.