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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)?

Apr 9, 2018

#1
+7545
+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

Apr 9, 2018

#1
+7545
+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