If the polynomial x^4-16x^2-25x+10 is divided by another polynomial x^2-2x+k, the remainder comes out to be x+a find k and a.
My approach: I tried dividing the first polynomial by the second and then equating the remainder to (x+a). It didn't work out. Are my calculations wrong or am i on the...
yes i see that not all composite numbers can be split into the products of only 2 primes. But the proof remains the same even if when the number can be split into " n" number of primes.
OK here is how i approached it:
n can either be a prime number or a composite
1) if n is prime:
a) assume root n is rational. therefore root n = p/q( where p, q are co-prime)
then n= p^2/q^2,
p^2= n *q^2
n divides p^2, therefore n divides p. Now for some integer k, p=nk...
thnx i understood ur method. I have just one more question:
How to prove that root n is irrational, if n is not a perfect square. Also, if n is a perfect square then how does it affect the proof.
Prove that cube root of 6 irrational.
Solution: I am trying to prove by contradiction.
Assume cube root 6 is rational. Then let cube root 6 = a/b ( a & b are co-prime and b not = 0)
Cubing both sides : 6=a^3/b^3
a^3 = 6b^3
a^3 =...