what is the solution set of the quadratic inequality $x^{2}-5leq0$?\n${x|-5leq xleq5}$\n${x|-sqrt{5}leq…

what is the solution set of the quadratic inequality $x^{2}-5leq0$?\n${x|-5leq xleq5}$\n${x|-sqrt{5}leq xleq5}$\n${x|-5leq xleqsqrt{5}}$\n${x|-sqrt{5}leq xleqsqrt{5}}$

what is the solution set of the quadratic inequality $x^{2}-5leq0$?\n${x|-5leq xleq5}$\n${x|-sqrt{5}leq xleq5}$\n${x|-5leq xleqsqrt{5}}$\n${x|-sqrt{5}leq xleqsqrt{5}}$

Answer

Explanation:

Step1: Rearrange the inequality

Add 5 to both sides of $x^{2}-5\leq0$ to get $x^{2}\leq5$.

Step2: Solve for x

Taking the square - root of both sides, we know that if $x^{2}\leq a$ ($a\geq0$), then $-\sqrt{a}\leq x\leq\sqrt{a}$. Here $a = 5$, so $-\sqrt{5}\leq x\leq\sqrt{5}$.

Answer:

${x|-\sqrt{5}\leq x\leq\sqrt{5}}$