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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
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
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