Problem on Quadratic inequalities

Question

If m is a real number and 2x^2+mx+8 has two distinct real roots, then what are the possible values of m? Express your answer in interval notation. Thanks

Answer 1

 2x²+mx+8=o has distinct real roots if m²-4*2*8>0

m²>64

√m²>√64

|m|>8

m<-8,  m>8

(-∞,-8), (8, +∞).

 

Answer 2

The discriminant must be positive.

 

b² - 4ac > 0 ⇒

 

m² - 4(2)(8) > 0

 

m² > 64

 

m > 8 or m < -8

 

In interval notation, you have (-∞,-8) ∪ (8,∞).