Question:
The number of solutions to the equation | x | (6x² + 1) = 5x² is
The number of solutions to the equation | x | (6x² + 1) = 5x² is
Updated On: Aug 21, 2024
- 7
- 9
- 8
- 5
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The Correct Option is D
Solution and Explanation
Scenario I: For x = 0 ,
It is evident that x = 0 satisfies the equation.
Scenario II: For x > 0,
considering : | x | (6x² + 1) = 5x²
⇒ x(6x² + 1) = 5x²
⇒ 6x² + 1 - 5x = 0.
Solving the quadratic equation, we find x = \(\frac{1}{2},\frac{1}{3}\) both of which are valid solutions.
Scenario III: For x < 0
considering : | x | (6x² + 1) = 5x²
⇒ -x(6x² + 1) = 5x²
⇒ 6x² + 5x + 1 = 0
Solving the quadratic equation, we obtain x = \(-\frac{1}{2},-\frac{1}{3}\), both of which are valid solutions.
Hence, there are a total of 5 solutions.
It is evident that x = 0 satisfies the equation.
Scenario II: For x > 0,
considering : | x | (6x² + 1) = 5x²
⇒ x(6x² + 1) = 5x²
⇒ 6x² + 1 - 5x = 0.
Solving the quadratic equation, we find x = \(\frac{1}{2},\frac{1}{3}\) both of which are valid solutions.
Scenario III: For x < 0
considering : | x | (6x² + 1) = 5x²
⇒ -x(6x² + 1) = 5x²
⇒ 6x² + 5x + 1 = 0
Solving the quadratic equation, we obtain x = \(-\frac{1}{2},-\frac{1}{3}\), both of which are valid solutions.
Hence, there are a total of 5 solutions.
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