How to solve these math problems?

Question

Simplify:

-3a(square root -112a^-1b^5c^21)

 

 

Find he x-intercepts and y-intercepts of each:

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

 

 

g(x)=2x-1/2x^2+5x-3

Answer 1

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

=-x(2x^2 -6x -9) = 0

x^2 -3x = 9/2

complete the square

x^2 -3x + 9/4 = 9/2 + 9/4

(x-3/2)^2 = 27/4

x-3/2 = + or - (3/2)sqr3

x= 3/2+(3/2)sqr3, 3/2 - (3/2)sqr3 and x=0

are 3 x intercepts

y intercept is y=0, the origin

g(x)= 2x -(1/2)x^2 +5x -3

= -x^2/2 +7x -3

y intercept is the constant term, y=-3

set g(x) =0 to solve for x intercepts

x^2 -14x + 6 = 0

complete the square

x^2 -14x + 49 =-6 +49

(x-7)^2 = 43

x =-7 + or - sqr43

sqr43 -7 = about 6.6-7 = -0.4

-sqr43 - 7 = about -6.6-7 = -13.6

those are the two x intercepts: -0.4 and -13.6

-3asqr(-112a^-1b^5c^21)

= sqr(-1008ab^5c^21)

= -12^b^2c^10(i)(7bc)^.5