What is the solutich set of the quadratic inequality 6x^2+1leqslant 0 7 xvert xin R xvert x=-(1)/(6) varnothing xvert x=(1)/(6)

To solve the quadratic inequality $6x^{2}+1\leqslant 0$, we first need to find the roots of the corresponding quadratic equation $6x^{2}+1=0$.<br /><br />The quadratic equation can be rewritten as $6x^{2}=-1$, which has no real solutions since the square of a real number cannot be negative.<br /><br />Therefore, the quadratic inequality $6x^{2}+1\leqslant 0$ has no real solutions, and the solution set is $\varnothing$.