Solve.
-$$x ^ { 2 } + 6

Question

Solve.
-$$x ^ { 2 } + 6 < 2 x$$
A) $\{ 2 \}$
B) $\varnothing$
C) $( - \infty , - 2 )$
D) $( 2 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $x^2 + 6 < 2x$, first rearrange it to get all terms on one side: $x^2 - 2x + 6 < 0$. The discriminant of this quadratic equation, $D = b^2 - 4ac = (-2)^2 - 4(1)(6) = 4 - 24 = -20$, is negative, indicating that the quadratic equation has no real roots. Since the coefficient of $x^2$ is positive, the parabola opens upwards, and because there are no real roots, the expression $x^2 - 2x + 6$ is always positive for all real $x$. Therefore, there are no real values of $x$ that satisfy the original inequality, making the correct answer $\varnothing$.

Solve - x2+6<2xx ^ { 2 } + 6 < 2 xx2+6<2x

Solve
- $x ^ { 2 } + 6 < 2 x$