Pesky Bi-Quadratic

Algebra Level 3

( x + 2 ) ( x + 3 ) ( x − 4 ) ( x − 5 ) = 60 (x+2)(x+3)(x-4)(x-5) = 60

Let the product of all possible values of x x be M M . Submit M M as your answer.


The answer is 60.

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Saqib M by Saqib M , 22, India

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3 solutions

William Isoroku
Aug 4, 2014

Since it's a quartic equation, the product of the roots is c/a.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Satvik Golechha
Jun 18, 2014

The product of roots of the equation will be (2 3 -4*-5)-60. Thus the answer is 60.

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Mohamed Hassan
Oct 20, 2015

(x+2)(x-4)(x+3)(x-5)=60

( x^2 - 2x - 8) ( x^2 - 2x - 15)=60

suppose that A= x^2 - 2 x

we get

(A - 8)(A - 15)=60

A^2 - 23A + 120=60

A^2 - 23A + 60=0

(A - 20)(A - 3)=0

A=20 , A=3

A=x^2 - 2x

x^2 - 2x - 3=0 , x^2 - 2x -20=0

by analyzing the equations above we get the roots

-1 , 3 , 1 - sqrt(21) , 1 + sqrt(21)

the products of the roots = 60

^^

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