Let `f(x)=ax^2+bx+c=0` has an irrational root r. If `u=p/q` be any rational number where a,b,c,p and q are integer. prove that `1/q^2<=|f(u)|`

Let f(x)=ax^(2)+bx+c=0 has an irrational root r. If u=(p)/(q) be any rational number where a a,b, p and q are integer.prove that (1)/(q^(2))<=|f(u)|

The reciprocal of any rational number (p)/(q) , where p and q are integers and q ne 0 , is

Prove that sqrt(p)+sqrt(q) is an irrational,where p and q are primes.

Is zero a rational number? Can you write it in the form (p)/(q) ,where p and q are integers and q!=0

In zero a rational number? Can you write it in the form (p)/(q), where p and q are integers and q!=0?

Express 0.123 as a rational number in the form of p/q, where p,p are integers,and q!=0

Let f(x)=Ax^(2)+Bx+c, where A,B,C are real numbers.Prove that if f(x) is an integer whenever x is an integer,then the numbers 2A,A+B, and C are all integer. Conversely,prove that if the number 2A,A+B, and C are all integers,then f(x) is an integer whenever x is integer.

Let f(x)=ax^(2)+bx+c, where a,b,c are rational,and f:z rarr z ,Where z is the set of integers.Then a+b is