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.

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

If p and q are the roots of the equation x^(2)+px+q=0 , then

The number of real roots of the equation |x|^(2)-3|x|+2=0 is

If p ,q ,r are positive and are in A.P., the roots of quadratic equation p x^2+q x+r=0 are all real for a. |r/p-7|geq4sqrt(3) b. |p/r-7|geq4sqrt(3) c. all p and r d. no p and r

Find the maximum possible number of real roots the equation . x^5-6x^2-4x+5=0

The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

Find the values of p so that the equation 2cos^2x-(p+3)cosx+2(p-1)=0 has a real solution.