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What is the value of b+c, when x^2+bx+c > 0 only when x E (-infty, -2) U (3,infty)?

Guest Apr 9, 2018

Best Answer 

 #1
avatar+7164 
+2

There is probably a better way to do this but here's one way....

 

x2 + bx + c  >  0   for  x  in the interval  (-∞, -2) U (3, ∞)

 

This implies that  x2 + bx + c  =  0  when  x  =  -2  and when  x  =  3

 

The equation of a parabola with zeros at  -2  and  3  is

 

y  =  a(x + 2)(x - 3)

 

y  =  a(x2 - x - 6)

 

y  =  ax2 - ax - 6a

 

Since the coefficient of  x2  in  x2 + bx + c  is  1  then  a = 1

 

x2 + bx + c   =   x2 - x - 6

 

b  =  -1     and     c  =  -6

 

b + c   =   -1 + -6   =   -7

hectictar  Apr 9, 2018
 #1
avatar+7164 
+2
Best Answer

There is probably a better way to do this but here's one way....

 

x2 + bx + c  >  0   for  x  in the interval  (-∞, -2) U (3, ∞)

 

This implies that  x2 + bx + c  =  0  when  x  =  -2  and when  x  =  3

 

The equation of a parabola with zeros at  -2  and  3  is

 

y  =  a(x + 2)(x - 3)

 

y  =  a(x2 - x - 6)

 

y  =  ax2 - ax - 6a

 

Since the coefficient of  x2  in  x2 + bx + c  is  1  then  a = 1

 

x2 + bx + c   =   x2 - x - 6

 

b  =  -1     and     c  =  -6

 

b + c   =   -1 + -6   =   -7

hectictar  Apr 9, 2018

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