Question

find the zeros of the polynomial 2 _/3x²+7x-5_/3, and verify the relationship between the zeroes and coefficients​

Answer 1

Explanation:

The given polynomial f(x)

= 4√3 x^2 +5x - 2√3

= 4√3 x^2 + 8x - 3x - 2√3

= 4x(√3 x +2) - √3 (√3 x +2)

= (√3x+2)(4x-√3)

Hence the zeroes are -2/√3 and √3/4

Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12

Sum of the roots = -b/a = -5/4√3 = -5√3/12

Hence sum of the roots =-b/a.

Product of the roots = (-2/√3)(√3/4) = -1/2.

Product of the roots = c/a = -2√3/4√3 = -1/2.

So product of the roots = c/a.