F(x)=-(x+1)^2+4 determine the nature of the roots

Answer 1

suppose you had f(x) = 4-x^2
The roots would be x = ±2

4-(x+1)^2 is the same graph, just shifted left by 1, so its roots are

x = -1±2 = -3,1

See

http://www.wolframalpha.com/input/?i=-%28x%2B1%29^2%2B4

Answer 2

Please help me to solve one/two of them, especially on how to determine the nature of roots of equation by not solving. E.g 3x sqrt-6x+9