Find the zeros of polynomial `f(x) = 4sqrt3 x^2 + 5x - 2sqrt 3`; and verify relation between zeros and its coefficient.

Explanation

Consider `4sqrt3 x^2 + 5x - 2sqrt 3 = 0`

`4sqrt3 x^2 + 8x - 3x - 2sqrt 3 = 0`

`4x(sqrt3 x + 2) - sqrt 3(sqrt3 x + 2) = 0`

`(sqrt3 x+2)(4x-sqrt3)=0`

`x=-2/sqrt3 or x = sqrt3/4`

Thus, `-2/sqrt3` and `sqrt3/4` are the zeroes of the polynomial of `4sqrt3 x^2 + 5x - 2sqrt 3`.

Let `alpha = -2/sqrt3` and `beta = sqrt3/4`

`alpha + beta = (-2/sqrt3) + (sqrt3/4) = (-8 + 3)/(4 sqrt 3)= -(5)/sqrt3 = -b/a`

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