If x y and z are three factors of a3 minus 7a minus 6 then the value of x y z is ........

Quantitative Aptitude ( CCS) Algebra

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If x, y, and z are three factors of a³−7a−6, then the value of x+y+z is,

-a

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Explanation:

Assuming the roots to be p, q and r we can form the equation,
(a−p)(a−q)(a−r)=a³−7a−6.
Now we do coefficient analysis. By the zero value of the coefficient of a², we deduce,
p+q+r=0.
Adding the three factors, (a−p), (a−q) and (a−r) we get,
3a−(p+q+r)=3a.