in a2+px+q, the roots are a and b, then a+b=-p and ab=q why????? Pls derive this!!!!!!!

x² + px + q = 0

a,b are the roots of this equation so x = a will satisfy this eq

at x = a

a² + pa + q = 0       ..............1

at x = b also satisfies this equation so

at x =b

b² + pb + q = 0           ..............2

subtracting both equations

(a²-b²) + p(a-b)) = 0

(a-b)[(a+b) + p] = 0 

 (a+b) = -p             ...........3       ans1

adding eq1 & eq2

a²+b² + p(a+b) + 2q = 0                                           [(a+b)² = a²+b² + 2ab]

 (a+b)²-2ab + p(a+b) + 2q = 0

from eq3 plugging value of a+b

  p² - 2ab - p² + 2q = 0

      q = ab     ...........4               ans2

hence , a+b = -p & ab = q