smc

We can rewrite the equation as $x^2+2hx-3=0.$ By Vieta's Formulas, the sum of the roots is $-2h$ and the product of the roots is $-3.$ Let the two roots be $r$ and $s.$ Note that $$r^2+s^2=(r+s{)}^2-2rs=(-2h{)}^2-2(-3)$$ Therefore, $4h^2+6=10$ and $h=\pm 1.$ This doesn't match any of the answer choices, so the answer is $\boxed{\text{None of these}}.$