Question

Let f (x) = px 2 + qx - 4 p, where p 0. Find the number of roots for the equation f (x) = 0 . Justify your answer.

Answer 1

f(x) = 0

px^2 + qx - 4p = 0

abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)

x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)

x = (-q ± √(q^2 + 4^2·p^2))/(2·p)

Because q^2 + 4^2·p^2 > 0 there are two roots.