Question

Product of the irretational roots of the equation (2x-1)(2x-3)(2x-5)(2x-7)=9

Answer 1

Answer:

Let 2x - 4 = y

=> (y + 3) (y + 1) (y - 1) (y - 3) = 9

=> (y^2 - 1) (y^2 - 9) = 9

=> y^4 - 10y^2 + 9 = 9

=> y^2 (y^2 - 10) = 0

=> y = 0 or ± √(10)

=> 2x - 4 = ± √(10)

=> x = (1/2) [4 ± √(10)]

=> product of the irrational roots

= (1/2)^2 * [4 + √(10)] [4 - √(10)]

= (1/4) * 6

= 3/2.