Matrices & Determinants
Properties of 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
(-2,1)
(-3,0)
(-3/2, 3/2)
(0,3)
Step-by-Step Solution
Key Concept: Expand the determinant and solve the resulting quadratic equation in alpha.
Expanding the determinant: 1(0 - (3α+1)(α+1/3)) - 3/2(0 - (2α+3)(α+1/3)) + (α+3/2)((3α+1) - 2/3(2α+3)) = 0. Simplifying this leads to a quadratic equation in α. Solving it gives the roots which lie in the interval (-3, 0).
Correct Answer: 2