equations and inequalities

Question

the inequality 0>2x² +bx +5 has an infinite number of real solutions when (which one):

 

a: -2√10<b<2√10

 

b: -2√10≤b≤2√10

 

c: b<-2√10 or b>2√10

 

d: b≤-2√10 or b≥2√10

Answer 1

For the solutions to be real, the discriminant must be positive or zero.

 

b^2 - 4(2)(5) >= 0

b^2 - 40 >= 0

 

 b^2 >= 40 = 6.32455532....

 

 The square root of 40 is in fact 2*sqrt(10)

 

b <= -2*sqrt(10) or b >= 2*sqrt(10)