Solve the absolute value equation or indicate that the equation has no solution.
-$\left| 2 x ^ { 2 } - x - 1 \right| = 3$
A) $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , \frac { 1 + \sqrt { 33 } } { 4 } \right\}$
B) $\left\{ - \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$
C) $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the equation $\left| 2x^2 - x - 1 \right| = 3$, we consider two cases: $2x^2 - x - 1 = 3$ and $2x^2 - x - 1 = -3$. Solving each case gives us the roots $\frac{1 - \sqrt{33}}{4}$ and $\frac{1 + \sqrt{33}}{4}$, which match option A.

Solve the Absolute Value Equation or Indicate That the Equation ∣2x2−x−1∣=3\left| 2 x ^ { 2 } - x - 1 \right| = 3​2x2−x−1​=3

Solve the Absolute Value Equation or Indicate That the Equation $\left| 2 x ^ { 2 } - x - 1 \right| = 3$