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 √(3)x^2+5x-2 √(3)=0\\ \\ \Delta=5^2-4*4 √(3)* (-2√(3) )\\ \\ \Delta=25+96=121\\ \\ x=(-5 \pm √(121))/(2*4 √(3) )=(-5 \pm 11)/(8 \sqrt3)\\ \\ x_1=(-5-11)/(8\sqrt3)=-(16)/(8\sqrt3)=-(16\sqrt3)/(24)=-(2\sqrt3)/(3)\\ \\ x_2=(-5+11)/(8\sqrt3)=(6)/(8\sqrt3)=(6\sqrt3)/(24)=(\sqrt3)/(4)\\`