Answer :
Answer:
[tex]x=\sqrt{3}-2\\x=-\sqrt{3}-2\\x=\frac{1}{2}[/tex]
Step-by-step explanation:
This is a hard one
We have to use the rational root theorem
[tex]2x^3+7x^2-2x-1[/tex] = 0
We have to find all the factors of a and d and put them in a fraction
[tex]a=2\\d=-1\\\frac{1}{1,2}[/tex]
We then plug them into the equation to see if any of them work
The equation isn't true when plugging 1, but is true when plugging in 1/2
factored form of 1/2 is (2x-1)
Then we divide the original equation by (2x-1) (you can use synthetic division or long division, it would be hard to type out the process for that) to get [tex]x^2+4x+1[/tex]
So now the equation is [tex](2x-1)(x^2+4x+1)[/tex]
Solve the second half of this equation using the quadratic formula to get
[tex]\sqrt{3}-2[/tex] and [tex]-\sqrt{3}-2[/tex]
We already know the solution for the first half of the equation (1/2)
So the final answers are:
[tex]x=\sqrt{3}-2, -\sqrt{3}-2, \frac{1}{2}[/tex]