The integral value of m for which the quadratic equation 2 m - 3 x 2 - 4 x + 2 m - 3 = 0 has both the roots negative is given by

Step-by-step solution

∵ Both roots are negative ∴ D > 0 , sum of roots → - v e , product of roots → + v e D > 0 ⇒ 16 - 4 2 m - 3 2 > 0 ⇒ 4 - 2 m - 3 2 > 0 2 - 2 m + 3 2 + 2 m - 3 > 0 ⇒ - 2 m + 5 2 m - 1 > 0 ⇒ 2 m - 5 2 m - 1 < 0 ⇒ 1 2 < m < 5 2 α + β < 0 ⇒ 4 2 m - 3 < 0 ⇒ m < 3 2 α β > 0 ⇒ 1 > 0 (always true) Taking intersection, we get, m ∈ 1 2 , 3 2 Integral value of m = 1