Question

If one root of the equation ax²+ bx+ c=0 be the square of the other, prove that b³+ a²c+ ac²= 3abc
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Answer 1

Acc. To Me,

I prove it below

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If you suppose one root m then other is m²

sum of roots=m+m²= -b/a------------1

prd of roots=m*m²=c/a     =>m³=c/a---------------2

Just cube the eq 1 and put value

(m+m²)³= -(b/a)³

m³+(m^6)+3m*m²(m+m²)= -(b/a)

Put the value of m³ and m+m² from eqs

c/a+(c/a)²+3c/a(-b/a)= -(b/a)

Take LCM and solve then you find

b³+a²c+ac²=3abc

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I hope you understand my answer

Answer 2

please see the attachment