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Shivam Bhagat Grade: 9
        in a2+px+q, the roots are a and b,   then    a+b=-p  and ab=q  why????? Pls derive this!!!!!!!
6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

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


 

6 years ago
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