Question

Find the zeroes of the polynomial f(x) = underoot 3x^2 +5x -8underroot3 and verify the relationship between the zeroes and its coefficients.

Answer 1

f(x) = √3x^2 +5 x -8√3

= √3x^2+8x-3x -8√3

=x(√3x+8) -(√3x+8)

=(√3x+8)(x-√3)

for zeros of f(x)

f(x) =0

(√3x+8)(x-√3)=0

x=-8/√3 or x=√3

sum of zeros=-5/√3

-8/√3+√3= -5/√3

-5/√3=-5/√3

product of zeros =-8√3/√3

-8/√3× √3= -8√3/√3

-8√3/√3=-8√3/√3

hence verified