5. Find m so that PoUlS UI6. Show that the roots of the equation x2+2(

1.	5. Find m so that PoUlS UI6. Show that the roots of the equation x2+2(3a+5) x + 2 (9 a2 + 25) -0 are complex unlessroots 0
Answer» For roots to be complex or real, we have to find the discriminant of the equation so, D = [2(3a+5)]²- 4(1)(18a²+50) = 4[ 9a²+30a+25-18a²-50] = 4[-9a²+30a-25] so, so, the value -9a²+30a-25 = -(9a²+25-30a) = -(3a-5)² = -ve of (sqaure) = always -ve so, this value will be always -ve.. but 0 only at a = 5/3. so D will always be -ve.. and hence complex solution.. unless D = 0 at a = 5/3.

5. Find m so that PoUlS UI6. Show that the roots of the equation x2+2(3a+5) x + 2 (9 a2 + 25) -0 are complex unlessroots 0

Answer»

For roots to be complex or real, we have to find the discriminant of the equation

so, D = [2(3a+5)]²- 4*(1)*(18a²+50) = 4[ 9a²+30a+25-18a²-50] = 4[-9a²+30a-25]

so, so, the value -9a²+30a-25 = -(9a²+25-30a) = -(3a-5)² = -ve of (sqaure) = always -ve

so, this value will be always -ve.. but 0 only at a = 5/3.

so D will always be -ve.. and hence complex solution.. unless D = 0 at a = 5/3.