Matrices & Determinants
Determinants
Grade Class 12
Question:
The values of α, for which <br><table><tr><td>1</td><td>3/2</td><td>α+3/2</td></tr><tr><td>1</td><td>1/3</td><td>α+1/3</td></tr><tr><td>2α+3</td><td>3α+1</td><td>0</td></tr></table> = 0, lie in the interval [JEE (Main) 2024]
(1) (-2,1)
(2) (-3,0)
(3) (-3/2, 3/2)
(4) (0,3)
Step-by-Step Solution
Key Concept: Evaluate the determinant by performing row operations or expanding along a row/column to find the roots of the resulting quadratic equation in alpha.
Expanding the determinant or simplifying using row operations R1 -> R1 - R2 gives a quadratic equation in α. Solving this equation yields the roots, which are then checked against the given intervals.
Correct Answer: (2)