I need help on this question please: x(x+3)(x+3)=0

Answer 1

x= 0 and x=-3

just set each factor = 0 and solve for x

x(x+3)(x+3) = 0

x= 0

x+3=0 subtract 3 from both sides to get x=-3

the roots, zeros, solutions or x intercepts are 0 and -3

if you graph x(x+3)(x+3) = 0, the curve intersects the x axis at x=0 or the origin, the point (0,0)

it also is tangent to the x axis, just touching it, but not crossing it, at x=-3, the point (-3,0)

You tell that from x(x+3)^2= 0 where the factor x+3 has an exponent of 2. the solution x=-3 has multiplicity 2

a 3rd degree equation has 3 solutions. maximum 3 real solutions, but -3 repeats.

x(x+3)(x+3) = x(x^2 +6x +9) = x^3 +6x^2 +9x = f(x) take the derivative and set = 0

f'(x) = 3x +12x + 9 = 0 divide by 3

x+4x+3 = 0 factor

(x+3)(x+1) = 0

x=-3 and x=-1 are where the curve has local or relative extrema, relative max or minimum points

that's the points (-3,0) and (-1,-4) plug the x values into f(x) to find the corresponding y coordinates

(-3,0) is a relative or local maximum

(-1,-4) is a relative or local minimum