The solution set of the quadratic inequality [tex]6x^2+1 \leq 0[/tex] is empty (∅).
What is inequality?
Inequality is a statement of an order relationship "greater than, greater than or equal to, less than, or less than or equal to" between two numbers or algebraic expressions.
What is the quadratic equation?
The equation whose highest degree of the variable is 2, then it is said to be a quadratic equation.
Solving the inequality:
Given quadratic inequality as [tex]6x^2+1 \leq 0[/tex]
Adding -1 on both sides (subtracting 1)
[tex]6x^2+1 -1 \leq 0 -1[/tex]
⇒ [tex]6x^2\leq -1[/tex]
Dividing with 6 both sides
⇒ [tex]x^2\leq \frac{-1}{6}[/tex]
Since the value is negative and the root for negative numbers is not defined, the given inequality has no solution.
Therefore, the solution set for the quadratic inequality [tex]6x^2+1 \leq 0[/tex] is an empty set (∅).
Learn more about inequalities here:
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