Question

solve the cubic equation x3-9x+28=0

Answer 1

${x}^{3} - 9x + 28 = 0 \\ x( {x}^{2} - {3}^{2} ) = - 28 \\ x( x - 3)(x + 3) = - 28 \\ x = - 28 \: or \\ x - 3 = - 28 \\ x = - 25 \: or \\ x + 3 = - 28 \\ x = - 28 - 3 = - 31$

Answer 2

${x}^{3} - 9x + 28 = 0$

$x _{1,2,3} = \omega _{k} \sqrt[3]{ - \frac{28}{2} + \sqrt{( \frac{28}{2} ) ^{2} - ( \frac{9}{3} ) ^{3} } } + \omega _{k} {}^{2} \sqrt[3]{ - \frac{ 28}{2} - \sqrt{( \frac{28}{2} ) ^{2} - ( \frac{9}{3} ) ^{3} } }$

$x_{1,2,3} = - \omega _{k} - 3 \omega _{k} {}^{2}$

$\implies x = - 4, \: 2 + \sqrt{3}i , \: 2 - \sqrt{3} i$

where, i = √(−1)