Question

Which 2 values of x are roots of the polynomial below?

Answer 1

Given:

The given polynomial is:

`f(x)=`
`3x^(2)-3x+1`

To find the roots of the given polynomial.

To find the roots we have to take
`f(x) = 0`

So,

`3x^(2) -3x+1 = 0`

Formula

By quadratic formula, the root of the equation
`ax^(2) +bx+c = 0` is,

`x = \frac{-b+\sqrt{b^(2)-4ac } }{2a}` and
`\frac{-b-\sqrt{b^(2) -4ac} }{2a}`

Now,

Putting,
`a=3, b=-3, c=1` we get,

`x = \frac{3+\sqrt{3^(2)-4(3)(1) } }{(2)(3)}` and
`\frac{3-\sqrt{3^(2)-4(3)(1) } }{(2)(3)}`

`x = (3+√(-3) )/(6)` and
`x=(3-√(-3) )/(6)`

Hence,

The values of the roots of the given polynomial are
`x=(3+√(-3) )/(6)` and
`x=(3-√(-3) )/(6)`

Hence, Option A and F are the correct answer.