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if a and b are the roots of the quadratic equation x^2+x+1 then give the equation whos roots are a^14 and b^26

if a and b are the roots of the quadratic equation x^2+x+1 then give the equation whos roots are a^14 and b^26

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2 Answers

pranay sharma
31 Points
9 years ago

a=-b

a2=b2

a14=(a2)7=m7

b26=(b2)13=(a2)13=m13

(x-m7)(x-m13)=0

x2-(m6+1)m7x+m20

x2-(a12+1)a14x+a40

Arjun Bhattacharya
20 Points
9 years ago

a=w, b=w^2 where w is a complex cube root of unity

a^14 = w^14 = (w^12).(w^2) = w^2

b^26 = w^52 = (w^51)(w)=w

therefore, the required equation is

x^2 - (w+w^2)x + (w^3)=0

=>x^2 + x + 1=0, that is, the given equation....

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