let P=cos(2pi/7)+isin(2pi/7). the complex number a=P+P^2+P^4 is a root of the quadratic equation x^2+ax+b=0, where a and b are real.
1. prove 1+P+P^2+.....P^6=0
2. find the values of the coefficients a and b
3. deduce that -sin(pi/7)+sin(2pi/7)+sin(3pi/7)=root 7 times 0.5
a missile was launched from the ground at an angle of 30, the initial velocity was 300 m/s
a)find the total flight time
b)what is the value of horizontal velocity at 20s
tangents from the pt P(m,n) touch the parabola x^2=8y at the pts A and B. show that the x-coordinates of A and B are the roots of the quadratic equation x^2-2mx+8n=0