If `p ,q in {1,2,3,4,5}` , then find the number of equations of form `p^2x^2+q^2x+1=0` having real roots.

If p,q,in{1,2,3,4}, then find the number of equations of the form px^(2)+qx+1=0 having real roots.

let p,q varepsilon(1,2,3,4), then number of equation of the form px^(2)+qx+1=0 ,having real roots is

Let alpha, beta be the roots of x^2-x+p=0 and gamma, delta be the roots of x^2-4x+q=0 such that alpha, beta, gamma, delta are in G.P. and pge2. If a,b,c epsilon {1,2,3,4,5}, let the number of equation of the form ax^2+bx+c=0 which have real roots be r, then the minium value of p q r =

If p,q,r and s are real numbers such that pr=2(q+s), then show that at least one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

Show that if p,q,r and s are real numbers and pr=2(q+s) , then atleast one of the equations x^(2)+px+q=0 and x^(2)=rx+s=0 has real roots.

Consider the equation of the form x^(2)+px+q=0 , then number of such equations that have real roots and have coefficients p and q in the set {1,2,3,4,5,6} (p may be equal to q) is

If p and q are roots of the equation 2x^2-7x+3 then p^2+q^2=