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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!!!!!!!

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

Grade:9

1 Answers

vikas askiitian expert
509 Points
10 years ago

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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