Question for math lovers -1
Algebra
Level
3
if root of the equation are a,b and those of are c,d then find the value of a+b+c+d (where a,b,c,d are distinct numbers)
1480
1110
1210
1340
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1 solution
Use Vieta's formulas. Therefore, a+b = -11d and c+d = -11b. Now, you can figure out that a+b+c+d = -11(d+b). That means the sum must be a multiple of 11. Than you use Vieta's formulas again to find ab = 10c and cd = 10a. d and b are both multiples of ten so that means the sum must be both a multiple of 11 and 10. I got 1210 as my answer.