Find the roots of the quadratic equation:
\$ 5x^2 = -5 \$

the equation is in the form of

\$ax^2+bx+c=0\$

the given equation is

\$ 5x^2 = -5 \$

move (-5) to left side

\$ 5x^2 +0x + 5 = 0 -> (1) \$

Since the equation (1) is in the form of

\$ax^2+bx+c=0\$

formula

\$ x = (-b \pm \sqrt (b^2 - 4ac))/(2a) \$

converting the equation into formula

\$ x = (-(0) ± \sqrt((0)^2 - 4\times(5)\times(5)))/(2\times(5)) \$

Simplifing the equation

\$ x = ( ± \sqrt(0 - 100))/10 \$

After simplification we get

\$ x = ( ± \sqrt( - 100))/10\$

We know that \$i^2 = -1\$

\$ x = ± \sqrt(i^2 10^2)/10 \$

Simplify the square root

\$ x = (± 10i)/10\$

After Cancellation we get

\$ x = (± \cancel(10)i)/\cancel(10) \$

after calculation

\$ x = ±i \$

Answer

D