If x^2-10ax -11b=0 have roots c and d x^2-10cx-11d have roots a and b, find the value of a+b+c+d
If has roots and and has roots and , then find the value of .
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1 solution
c+d=10a cd=-11b
a+b=10c ab=-11d
Adding above two
a+b+c+d=10(a+c)
b+d=9(a+c)
subtracting above two
(c-a)+(d-b)=10(a-c)
b-d=9(c-a)
Dividing above two
(c+d)/(a+b)=a/c
c^2-a^2=ab-cd
(c-a)(c+a)=-11d+11b
Solving these we get a+b+c+d=10(a+c)=1210