Question

How many unique values of x solve x3 + 8x2 + 16x = 0?
N =

Answer 1

${x}^{3} + {8x}^{2} + 16x = 0 \\ {x}^{3} + {8x}^{2} + {8x}^{2} + 16x = 0 \\ {x}^{3} + 16x + {8x}^{2} + {8x}^{2} = 0 \\ {x}( {x}^{2} + 16) + {8x}^{2} (1 + 1) = 0$

Answer 2

${x}^{3} + 8 {x}^{2} + 16x = 0$
lets take x as common from.all the number

$x( {x}^{2} + 8x + 16) = 0 \\ x( {x}^{2} + 4x +4x+ 16) = 0 \\ x( (x(x+4)+4(x + 4)) = 0 \\x(x+4)(x + 4) = 0 \\ x{(x + 4)}^{2} = 0 \\ x = 0 \: \: x = - 4 , -4$
total 3 values are 0 , -4 & -4 but -4 is repeated so only two unique values