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If x^2-10ax-11b =0 have roots c and d. x...

If `x^2-10ax-11b =0` have roots c and d. `x^2-10cx -11d=0` have roots a and b, then find a+b+c+d.

Text Solution

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The correct Answer is:
1210
Here, `a+b=10cand c+d=10a`
`implies(a-c)+(b-d)=10(c-a)`
`implies(b-d)=11(c-a)" "...(i)`
Since, 'c' is the root of `x^(2)-10ax-11n=0`
`implies c^(2)-10ac-11b=0" "(ii)`
Similarly, 'a' is the root of
`x^(2)-10cx-11d=0`
`implies a^(2)-10ca-11d=0" "...(iii)`
On subtracting Eq. (iv) from Eq. (ii), we get
`(c^(2)-a^(3))=11(b-d)" "...(iv)`
`therefore(c+a)(c-a)=11xx11?(c-a)" "["from Eq.(i)"]`
`impliesc+a=121`
`thereforea+b+c+d=10c+10a=10(c+a)=1210`
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