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the roots of the equation x^2+(p+2)x+2p=0 are distinct integers when |
| Answer» x2+(p+2)x+2p=0On comparing with ax2+bx+c=0 we geta=1 b=p+2 c=2pNow since roots of the given quadratic equation are distinct integer.Therefore, Discriminent D=b2-4ac > 0 (p+2)2-4×1×2p > 0 p2+2×p×2+22\xa0-8p > 0 p2+4p+4-8p > 0 p2\xa0-4p +4 > 0 p2-2p-2p+4 > 0 p(p-2)-2(p-2) > 0 (p-2)(p-2) > 0 (p-2)2\xa0> 0 p-2 > 0 p > 2So roots of the given quadratic eq. is distinct integer if p>2. | |