Question

Suppose we know that the polynomial equation 4x^3 − 12x²+3x +5 =0 has three real solutions and that one of the factors of 4x^3 − 12x²+ 3x+5 is (x − 1). How can we find all three solutions to the given equation?

Answer 1

So three solution of the equation are x = 1 , 2.5, -0.5

Explanation:

We have given equation
`4x^3-12x^2+3x+5`

We have given that (x-1) is a factor of this polynomial so it will completely divide the polynomial

So after division
`(4x^3-12x^2+3x+5)/(x-1)=4x^2-8x-5`

So two other factor of polynomial will be the root of
`4x^2-8x-5`

`4x^2-8x-5=(x-2.5)(x+0.5)`

So three solution of the equation are x = 1 , 2.5, -0.5