Question

What is the solution set of the quadratic inequality 6x2 + 1 <_ 0

Answer 1

Answer:

No solution.

The solution set is $\left \{ \phi \right \}$

Step-by-step explanation:

We have been given the quadratic inequality $6x^2+1\leq 0$

Subtract 1 to both sides

$6x^2+1-1\le \:0-1\\\\6x^2\le \:-1$

Divide both sides by 6

$\frac{6x^2}{6}\le \frac{-1}{6}\\\\x^2\le \:-\frac{1}{6}$

Now, we know that square of a number always gives positive values.

Thus, the above result never hold true for any real values of x.

Therefore, the inequality has no solution.

Hence, the solution set is $\left \{ \phi \right \}$

Answer 2

Answer : $x^2\leq -1/6$

Explanation:

$6x^2 +1 \leq 0$

shifting 1 to Right hand side becomes -1

$6x^2\leq -1$

shifting 6 on right hand side will divide -1 becomes -1/6

$x^2\leq -1/6$

Quadratic equation is the equation having degree 2 and inequality which is not  equal  to right hand side