Question
Question: If a and b are the roots of the quadratic equation x<sup>2</sup> + x + 1 = 0, then the equation whos...
If a and b are the roots of the quadratic equation x2 + x + 1 = 0, then the equation whose roots are a2000, b2000 is:
A
x2 + x –1 = 0
B
x2 + x + 1 = 0
C
x2 – x + 1 = 0
D
x2 – x –1 = 0
Answer
x2 + x + 1 = 0
Explanation
Solution
a = w then b = w2
Ž a2000 = (a3)666. a2 = w2
b2000 = (b3)666 . b2 = w
Thus equation is x2 – (w + w2) x + 1 = 0
Ž x2 + x + 1 = 0
Hence choice (2) is true.