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)|`

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

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

If p(q-r) x^2 +q(r-p) x+r(p-q) =0 has equal roots then 2/q =

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

If x^(2)+px+q=0 is the quadratic equation whose roots are a-2 and b-2 where a and b are the roots of x^(2)-3x+1=0, then p-1,q=5 b.p=1,1=-5 c.p=-1,q=1 d.p=1,q=-1

Find the condition that the roots of cubic equation x^3+ax^2+bx+c=0 are in the ratio p : q : r .

If the roots of the quadratic equation ax^2 + cx + c = 0 are in the ratio p :q show that sqrt(p/q)+sqrt(q/p)+sqrt(c/a)= 0 , where a, c are real numbers, such that a gt 0