Homework questions #4

Question

1. Without solving, does -.5x-3x+2=5 have real solutions? (Yes or no)
2. Solve -.5x+3x+2=5 to show the nature of its roots

Answer 1

You probably meant: -0.5x^2 -3x +2 = 5 which is the same as

x^2 +6x + 6 = 0

the discriminant = b^2 -4ac = 36-24 > 0, so it has 2 real solutions

then the next part has +3x instead of -3x, could be a typo

but that would translate into x^2 -6x +6 = 0

complete the square

(x-3)^2 = -6+9 = 3

x = 3 + or - sqr3 = 4.7 or 1.3

or use the quadratic formula

with x = 6/2 + or - (1/2)sqr(36-24) = 3 + or - (1/2)sqr12 = 3 + or - sqr3 = 4.732 or 1.268 = about 4.7 or 1.3

two real solutions