Question

find zeros of quadratic polynomial 6x^2-3-7x and verify the relationship between the zeroes and cofficientof the polynomial

Answer 1

6x^2-7x-3=0
let it be....px^2+qx+r=0
6x^2-9x+2x-3=0
3x (2x-3)+1 (2x-3)=0
(2x-3)(3x+1)=0
so we get
x=3/2 or x=-1/3
name both as a=3/2 and b=-1/3
now
if we add them
a+b=7/6 that is nothing but the negative coefficient of x upon coefficient of x^2
so we formulate it as a+b= -q/p

similarly if we multiply the roots
ab= 3/2 × (-1/3)
ab= -1/2
which is constant term upon coefficient of x^2
so ab= r/a

that's how the coefficient and the roots are related...
hope it will help you.