Algebra Question #8

Algebra Level 2

The roots of x 2 − x + 1 = 0 x^{2} - x + 1 = 0 is "r" and "s" and the roots of a x 2 + b x + c = 0 ax^{2} + bx + c = 0 is " r 100 r^{100} " and " s 100 s^{100} ". Find c / a c / a .

Algebra Question


The answer is 1.

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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3 solutions

Paul Ryan Longhas
Nov 22, 2014

x^{2} - x + 1 = 0 -----> rs = 1 and ax^{2} + bx + c = 0 -----> c / a = (rs)^100 = 1^100 = 1 answer

1 Helpful 0 Interesting 0 Brilliant 0 Confused

With the formula it is all right rs=c/a , but using Shridharacharya's eq. all results are imaginary, so there must be some mistake in the first Equation.

Aditya Paul - 6 years, 3 months ago
Ivander Jonathan
Feb 18, 2015

Using vieta's formula, r s = 1 rs=1 . Again, ( r s ) 100 = c a (rs)^{100}=\frac{c}{a} . Using substitution, 1 100 = c a = 1 1^{100}=\frac{c}{a}=1 .

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Ameya Ballal
Nov 23, 2014

highly over rated question . It should deserves level 1 or 2 but definitely not 4.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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