Question

For a certain equation, `a, b, c` belongs to real numbers. `ab > 0` and `a+2b+4c=0`. Then, the equation `ax^2+bx+c=0` has what kind of roots (one +ve & one -ve, both +ve or both -ve) ? Thank you!

Answer 1

See below.

Explanation:

Putting `c=-(a+2b)/4` into

`a x^2+b x + c = 0` and solving for `x` we obtain

`x = -(bpm(a+b))/(2a)= {(1/2),(-(1/2+b/a)):}`

so if `ab > 0` we have two real distinct roots, with opposite signs.