Question

Find the zeroes of the polynomial f(x) = `2sqrt(3)x^2 - 5x + sqrt(3)` and verify the relation between its zeroes and coefficients.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

`2sqrt(3)x^2 - 5x + sqrt(3)`

Answer 1

`2sqrt(3)x^2 - 5x + sqrt(3)`

⇒ `2sqrt(3)x^2 - 2x - 3x + sqrt(3)`

⇒ `2x(sqrt(3)x - 1) - sqrt(3)(sqrt(3)x - 1) = 0`

⇒ `(sqrt(3)x - 1) = 0` or `(2x - sqrt(3)) = 0` 

⇒ `x = 1/sqrt(3)` or `x = sqrt(3)/2` 

⇒ `x = 1/sqrt(3) xx sqrt(3)/sqrt(3)` = `sqrt(3)/3` or `x = sqrt(3)/2` 

Sum of zeroes = `sqrt(3)/3 + sqrt(3)/2`

= `(5sqrt(3))/6`

= `(-("Coefficient of"  x))/(("Coefficient of"  x^2))` 

Product of zeroes = `sqrt(3)/3 xx sqrt(3)/2`

= `sqrt(3)/6`

= `("Constant term")/(("Coefficient of "x^2))`