Question

find the cubic solution of x3 + x2 - 20x + 18​

Answer 1

Step-by-step explanation:

By observation one root of the the given expression is 1.

So,

On dividing (x³+x²-20x+18) by (x-1)

We have, (x³+x²-20x+18) = (x-1)(x²+2x-18)

Now, here we have to consider, x²+2x-18

It can't be factorised further by middle term splitting..

Hence by applying quadratic formula we have,

For the eqⁿ- x²+2x-18 = 0

x = [-2±sqrt{(-2)²-4(1)(-18)}]/2

On simplification, we get

x = -1±sqrt(19)

Therefore, another set of root for the eqⁿ are => (x-1+sqrt(19)), (x-1-sqrt(19))

So the given expression becomes =>

(x³+x²-20x+18) = (x-1)(x-1+sqrt(19))(x-1-sqrt(19))

Therefore, all the solutions for x are => (x-1), (x-1+sqrt(19), (x-1-sqrt(19))