Question

find the zeros of the polynomial f(x) = 4 root 3x^2 +5x -2root3 and verify the relationship between zeroes and coefficients

Answer 1

Explanation:

I will rewrite your "f(x) = 4 root 3x^2 +5x -2root3" as

f(x) = 4√3·x^2 +5x - 2√3

and then identify the coefficients of this quadratic. They are:

a = 4√3, b = 5, c = -2√3.

Next we'll find the "discriminant," b²-4ac:

(5)² - 4(4√3)(-2√3) = 25 + 32(3) = 25 + 96 = 121

The roots are:

-b ± √(discriminant) -5 ± √121 -5 ± 11

x = -------------------------------- = --------------- = --------------

2a 2(4√3) 8√3