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If one root of x2+px+q=0 may be the square of the other,then p3+q2 |
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Answer» Answer: HOPE it helps Step-by-step EXPLANATION: For QUADRATIC equation ax2+bx+c=0 : sum of roots =−b/a product of roots =c/a If ONE root of the equation x2+px+q=0 is the square of the other, then roots are ω and ω2 sum of roots =−p⟹p=−ω2−ω product of roots =q⟹q=ω2⋅ω=ω3 p3−q(3p−1)+q2 =(−ω2−ω)3−ω3(3(−ω2−ω)−1)+(ω3)2 =(−ω(ω+1))3−ω3(−3ω2−3ω−1)+ω6 =−ω3(ω3+3ω2+3ω+1)+3ω5+3ω4+ω3+ω6 =−ω6−3ω5−3ω4−ω3+3ω5+3ω4+ω3+ω6 =0 |
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