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blsea [12.9K]
3 years ago
10

Solve 2x^3+7x^2-2x-1=o​

Mathematics
1 answer:
Mashcka [7]3 years ago
8 0

Answer:

x=\sqrt{3}-2\\x=-\sqrt{3}-2\\x=\frac{1}{2}

Step-by-step explanation:

This is a hard one

We have to use the rational root theorem

2x^3+7x^2-2x-1 = 0

We have to find all the factors of a and d and put them in a fraction

a=2\\d=-1\\\frac{1}{1,2}

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 x^2+4x+1

So now the equation is (2x-1)(x^2+4x+1)

Solve the second half of this equation using the quadratic formula to get

\sqrt{3}-2 and -\sqrt{3}-2

We already know the solution for the first half of the equation (1/2)

So the final answers are:

x=\sqrt{3}-2, -\sqrt{3}-2, \frac{1}{2}

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