Question

solve for x:. x^3 - 67x +126 =0​

Answer 1

Answer:

The roots are 2,7,-9

Step-by-step explanation:

${x}^{3} - 67x + 126 = 0$

From observation we see one of the roots is x=2

so the cubic polynomial can be written as

$(x - 2)( a{x}^{2} + bx + c) \\ = a {x}^{3} + (b - 2a) {x}^{2} + (c - 2b)x - 2c$

Comparing with original equation we have

$a = 1 \\ b = 2 \\ c = - 63$

i.e the equation can be written as,

$(x - 2)( {x}^{2} + 2x - 63) = 0$

so one root is x=2 and other two roots are the roots of equation

$( {x}^{2} + 2x - 63) = 0$

Now roots of the above equation using quadratic formula is,

$x = - 9 \\ x = 7$

So finally the roots are

$x = 2 \\ x = - 9 \\ x = 7$