Solve the equation 4x^3 + 4x^2-x-1 = 0 given that -1/2 is a zero of f(x) = 4x^3 + 4x^2-x-1.

The solution of  equation 4x^3 + 4x^2-x-1 = 0 given that -1/2 is a zero of f(x) = 4x^3 + 4x^2-x-1 is

Solution:

Given, cubic equation

And is a zero of

We have to find the other two roots of the given quadratic equation.

Let the other two roots be a, b.

Now, we know that, sum of roots of cubic equation

Now, product of roots of cubic equation

substitute above value in this formula

Now, solve (1) and (2)

substitute "a" value in (1)

Hence, the roots of the given cubic equation are

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