Find the number of irrational roots of the equation (x-1)(x-2)(3x+1)(3x-2)=21

Asked by samiddhamukherjee | 25th Sep, 2010, 01:21: PM

Expert Answer:

the given polynomial after multiplying becomes
9x4-30x3+25x2-25
the possible rational zeroes can be found as follows
if p/q is a rational zero of the polynomial, (p and q are coprimes)
then,
p divides 25
q divides 9
so possible values  of p are
1,-1,5,-5,25,-25
possible values of q are
1,-1,3,-3
now form possible values of the rational roots
e.g.
1,-1,1/3, -1/3 etc
try factor theorem for them.
[if p(a) =0, then a is a factor of p(x)]
this way you will get how many rational roots are there.
divide y the product of those rational roots to the polynomial , then factorise the quotient so obtained.
then you will get the answer.

Answered by  | 27th Sep, 2010, 08:42: PM

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