If the quadratic equation ( +2)x^2-3 x+4 =0 , -2 , has two positive roots, then the number of possible integral values of is:

Step-by-step solution

For the quadratic equation ( +2)x^2-3 x+4 =0 to have two positive roots, the following three conditions must be satisfied: 1. Discriminant D 0 (-3 )^2 - 4( +2)(4 ) 0 9 ^2 - 16 ^2 - 32 0 -7 ^2 - 32 0 7 ^2 + 32 0 (7 + 32) 0 [- 32 7 , 0 ] 2. Sum of roots > 0 + = 3 +2 > 0 (- , -2) (0, ) 3. Product of roots > 0 = 4 +2 > 0 (- , -2) (0, ) Taking the intersection of all three conditions, we get: [- 32 7 , -2 ) Since - 32 7 -4.57 , the possible integral values of in this interval are -4 and -3 . Thus, there are 2 possible i