Question

Solve the equations:

(i) 6x⁴ – 35x³ + 62x² – 35x + 6 = 0

(ii) x⁴ + 3x³ – 3x – 1 = 0

Answer 1

(i) 6x⁴ – 35x³ + 62x² – 35x + 6 = 0 ….. (1) 

It is a even degree reciprocal equation as p(x) = xⁿp(1/x) 

Dividing equation (1) by x²,

Case (i): 

(ii) x⁴ + 3x³ – 3x – 1 = 0 …… (1) 

It is an even degree reciprocal function of type II. 

1, -1 are the solution of equation (1) 

(x – 1), (x + 1) are the factor of (1) 

(x² – 1) is a factor of (1) 

Dividing (1) by (x² – 1) we get, 

x² + 3x + 1 = 0 is the other factor.