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a) x^(2) + 6x + 1 = 0 (x + 3)^(2) - 8 = 0 x = - 3 + sqrt(8) or x = - 3 - sqrt(8)

b) (x-5)(x+1) = 0 x = -1 or 5

c) using answer to part b: (x-5)(x+1) < 0 draw its graph then: -1<x<5<...

integrating a product of functions of x - integration by parts. integral of uv' = uv - integral of u'v. choice of u from LIATE - logs, inverse trig, algebra, trig, exponentials - choose u=x. u=x, v'=e^(-x...

If the lines intersect the position vectors r_1 and r_2 must be equal at the point of intersection, so: (1,-1,2)+a(-1,3,4)=(c,-4,0)+b(0,3,2) which gives three equations for the three components: 1-a=c, -1...

[add 4 to both sides] 2x=10 Therefore, x=5

find sum of both equations: 14a=42, therefore a=3, substitute 'a' into an equation: (5x3)+2b=23, therefore 2b=8, therfore b=4