Quant Boosters - Hemant Malhotra - Set 11


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    general term = 8!/r1! * r2! * r3! * (1)^r1 * (x^2)^r2 * (-x^3)^r3
    = 8!/r1! * r2! * r3! * x^(2r1) * (-1)^r3 * (x)^3r3
    = 8!/r1! * r2! * r3! * (-1)^r3 * x^(2r2+3r3)
    now we have to find coefficient of x^6 here (for any coefficient same procedure )
    so r1 + r2 + r3 = 8
    2r2 + 3r3 = 6
    find r1, r2 and r3 here
    let r3=0 so r2=3 so r1=2 and let r3=2,so r2=0 so r1=6 (r1,r2,r3 should be integer because term can't be negative)
    now coefficient will be 8!/r1! * r2! * r3! *(-1)^r3
    put both values of r1,r2 and r3 and add
    so 8!/5! * 3!+8!/2! * 6!=84



  • @hemant_malhotra as the no. of real roots is asked so it will always be 3


 

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