which of the following equation has roots of the same sign ?

Question

1. x² + 2x -7 = 0
2. 3x² -x +3 = 0
3. x² +9x -1 =0
4. x² +3x -1 =0
5. x² -3x +1 =0

I want to know how to determine the sign or roots by equations.

Answer 1

For both solutions to have the same sign the constant in both factors have to have the same sign

which means that the last term of the quadratic must also be positive. If the last term is negative then the expression would factor to (x+a)(x-b) which eliminates #1,3and4

Equation #2 has no real solutions ( discriminators is <0) and so solutions will be in the form of a +bi, a -bi

where i is square root if (-1)

So that leaves only #5