If `x^2-2rp_rx+r=0; r=1, 2,3` are three quadratic equations of which each pair has exactly one root common, then the number of solutions of the triplet `(p_1, p_2, p_3)` is

If x^(2)-2rp_(r)x+r=0;r=1,2,3 are three quadratic equations of which each pair has exactly one root common,the number of solutions of the triplet (p_(1),p_(2),p_(3)) is

If the quadratic equation 4 x^ 2 - (p-2)x+ 1 = 0 has equal roots, then the value of 'p' are

Consider three quadratic equations, x^2-2r p_r x+r=0; r=1,2,3, Given that each pair has exactly one root common. The common root between the equations obtained by r=1a n dr=3 is (a) -sqrt(3/2) or sqrt(3/2) (b) -sqrt(2/3) or sqrt(2/3) (c) -sqrt(6) or sqrt(6) (d) 1

Suppose two quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 have a common root alpha , then a_(1)alpha^(2)+b_(1)alpha+c_(1)=0 " " …..(1) and a_(2)alpha^(2)+b_(2)alpha+c_(2)=0 " " ……(2) Eliminating alpha using crose - multiplication method gives us the condition for a common root Solving two equations simultaneously, the common root can be obtained. Now, consider three quadratic equations, x^(2)-2r p_(r )x+r=0, r=1, 2, 3 given that each pair has exactly one root common. In the notations of above problem, (gamma)/(alpha) is equal to

If p,q,r in R and the quadratic equation px^(2)+qx+r=0 has no real root,then

For what values of p the quadratic equation 3x^(2) + 12x + 4p = 0 has equal roots?

Find p in R for which x^2-px+p+3=0 has one root>2 and the other root<2.

Find the cubic equation whose roots are the squares of the roots of the equation x^3 +p_1 x^2 +p_2 x+p_3 =0

Find the cubic equation whose roots are the squares of the roots of the equation x^3 +p_1 x^2 +p_2 x+p_3 =0