1.

Obtain all zeros of `(3x^4 -15x^3 + 13x^2 +25x -30)`, if two of its zeros are`sqrt(5/3) and - sqrt(5/3)`.

Answer» Here, `f(x) = 3x^4 - 15x^3+13x^2+25x - 30`
As, `sqrt(5/3) and -sqrt(5/3)` are two of the zeroes of the `f(x)`.
`:. (x - sqrt(5/3)) and (x+sqrt(5/3))` are the factors of `f(x)`.
`=>(x^2-5/3) ` is the factor of `f(x)`.
Now, we can write,
`3x^4 - 15x^3+13x^2+25x - 30 = 3x^2(x^2-5/3)-15x(x^2-5/3)+18(x^2-5/3)`
`= (x^2-5/3)(3x^2-15x+18)`
`= (3x^2-5)(x^2-5x+6)`
`= (3x^2-5)(x-2)(x-3)`
So, remaining zeroes of `f(x)` are `2` and `3`.


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