Question

find the zeroes of the polynomial f(x)=4√3x²+5x-2√3,and verify the relationship between the zeroes and its co-efficients

Answer 1

$4 \sqrt{3}x^2+5x-2 \sqrt{3}=0\\ \\ \Delta=5^2-4*4 \sqrt{3}* (-2\sqrt{3} )\\ \\ \Delta=25+96=121\\ \\ x=\frac{-5 \pm \sqrt{121}}{2*4 \sqrt{3} }=\frac{-5 \pm 11}{8 \sqrt3}\\ \\ x_1=\frac{-5-11}{8\sqrt3}=-\frac{16}{8\sqrt3}=-\frac{16\sqrt3}{24}=-\frac{2\sqrt3}{3}\\ \\ x_2=\frac{-5+11}{8\sqrt3}=\frac{6}{8\sqrt3}=\frac{6\sqrt3}{24}=\frac{\sqrt3}{4}$