Question

Find the zeroes of the quadratic polynomial `f(x) = 4sqrt(3)x^2 + 5x - 2sqrt(3)`.

Write the zeros of the quadratic polynomial `f(x) = 4sqrt(3)x^2 + 5x - 2sqrt(3)`.

Answer 1

To find the zeroes of the quadratic polynomial we will equate f(x) to 0

∴ f(x) = 0

⇒ `4sqrt(3)x^2 + 5x - 2sqrt(3) = 0`

⇒ `4sqrt(3)x^2 + 8x - 3x - 2sqrt(3) = 0`

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

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

⇒ `x = -2/sqrt(3)` or `x = sqrt(3)/4` 

Hence, the zeroes of the quadratic polynomial `f(x) = 4sqrt(3)x^2 + 5x - 2sqrt(3)` are `-2/sqrt(3)` or `sqrt(3)/4`.