Question
Mathematics Question on Sequence and series
If α and β are the roots of the equation x2 + x + 1 = 0, then the equation whose roots are α19 and β7 is
A
(A) x2 – x – 1 = 0
B
(B) x2 – x + 1 = 0
C
(C) x2 + x – 1= 0
D
(D) x2 + x + 1 = 0
Answer
(D) x2 + x + 1 = 0
Explanation
Solution
Explanation:
α and β are the roots of x2+x+1=0 α=ωβ=ω2α19=ωβ7=ω2x2−(α19+β′)x+α19β7=0Thou,x2−(ω+ω2)x+ω⋅ω2=0x2+x+1=0