What are the zeros of f(x)=2x^3+3x^2-9x?

ANSWER[tex]x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3[/tex]EXPLANATIONThe given polynomial function is[tex]f(x) =2{x}^{3} + 3 {x}^{2} - 9x[/tex]To find the zeros, we equate the function to zero.[tex]2{x}^{3} + 3 {x}^{2} - 9x = 0[/tex]Factor x,[tex]x(2 {x}^{2} + 3x - 9) = 0[/tex]Split the middle term,[tex]x(2 {x}^{2} + 6x - 3x - 9) = 0[/tex][tex]x(2x(x + 3) - 3(x + 3) = 0[/tex][tex]x(2x - 3)(x + 3) = 0[/tex][tex]x=0,2x-3=0,x+3=0[/tex][tex]x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3[/tex]