Question

Solve 2x3 + x2 – 13x + 6 = 0( cubical equation)
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Answer 1

2(3)+x2-13x+6=0

6+2x-13x+6

12-11x=0

12+0=11x

12=11x

12/11=x

Answer 2

$\sf 2 {x}^{3} + {x}^{2} - 13x + 6 = 0$

$\sf 2 {x}^{3} - 4 {x}^{2} + 5 {x}^{2} - 10x - 3x + 6 = 0$

$\sf 2 {x}^{2} (x - 2) + 5x(x - 2) - 3(x - 2) = 0$

$\sf (x - 2)(2 {x}^{2} + 5x - 3) = 0$

$\sf (x - 2)(2 {x}^{2} + 6x - x - 3) = 0$

$\sf (x - 2)(2x(x + 3) - (x + 3)) = 0$

$\sf (x - 2)(x + 3)(2x - 1) = 0$

$\bf \implies\underline{ \: x_{1,2,3} = 2, - 3, \frac{1}{2}}$