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 p x^2+q x+1=0 having real roots.

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

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 =

Find the roots of the equations. Q. x^(2)-2x+5=0

Find the roots of the equations. Q. 2x^(2)+x-3=0

Find the roots of the equations. Q. 5x^(2)-x+4=0 .

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

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

If p,q,r,s are real and prgt4(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.