if the roots of the equation ` z^(2) + ( p +iq) z + r + is =0` are real wher p,q,r,s, `in` ,R , then determine ` s^(2) + q^(2)r`.

For a complex number z, the equation z^(2)+(p+iq)z+ r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2)-1 ), then

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

find the condition that px^(3) + qx^(2) +rx +s=0 has exactly one real roots, where p ,q ,r,s,in R

For p, q in R , the roots of (p^(2) + 2)x^(2) + 2x(p +q) - 2 = 0 are

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

If the roots of the equation 1/(x+p)+1/(x+q)=1/r are equal in magnitude and opposite in sign, then (A) p+q=r (B)p+q=2r (C) product of roots=- 1/2(p^2+q^2) (D) sum of roots=1

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

In Figure, O P||R S . Determine /_P Q R

If the equation (p+iq)x^2 +(m+ni)x+r=0 has real root where p,q,m, n and r are real (!=0) then pn^2+rq^2-mnq= (A) 1 (B) 0 (C) -1 (D) none of these