An algebra problem by Ossama Ismail

Algebra Level 2

If \(a,\) \(b,\) and \(c\) are real numbers such that \(a^2 + b^2 + c^2 = 1,\) then what is the minimum value of \(ab + bc +ca? \)

\[-1\] \[ - \frac{2}{3} \] \[ - \frac{1}{2} \] \[ -\frac{1}{4} \] \[ \frac{1}{4} \] \[ \frac{1}{2} \] \[1\]