(x^(2))/((p+qx)^(2))

The expression x^(2)-4px+q^(2)>0 for all real x and also r^(2)+p^(2)

Solve for x and y, px + qy = 1 and qx + py = ((p + q)^(2))/(p^2 + q^2)-1 .

If alpha and beta are the zeros of the polynomial f(x)=x^(2)+px+q, then a polynomial having (1)/(alpha) and (1)/(beta) is its zeros is (a) x^(2)+qx+p( b) x^(2)-px+q(c)qx^(2)+px+1 (d) px^(2)+qx+1

The equation x^(2) + px +q =0 has two roots alpha, beta then Choose the correct answer : (1) The equation qx^(2) +(2q -p^(2))x +q has roots (1) alpha /beta , beta/alpha (2) 1/alpha ,1/beta (3) alpha^(2), beta^(2) (4) None of these (2) The equation whose roots are 1/alpha , 1/beta is (1) px^(2) + qx + 1 =0 (2) qx^(2) +px +1 =0 (3) x^(2) + qx + p =0 (4) qx^(2) +x+ p =0 3. the values of p and q when roots are -1,2 (1) p = -1 , q = -2 (2) p =-1 , q =2 (3) p=1 , q = -2 (4) None of these

The equation x^(2) + px +q =0 has two roots alpha, beta then Choose the correct answer : (1) The equation qx^(2) +(2q -p^(2))x +q has roots (1) alpha /beta , beta/alpha (2) 1/alpha ,1/beta (3) alpha^(2), beta^(2) (4) None of these (2) The equation whose roots are 1/alpha , 1/beta is (1) px^(2) + qx + 1 =0 (2) qx^(2) +px +1 =0 (3) x^(2) + qx + p =0 (4) qx^(2) +x+ p =0 3. the values of p and q when roots are -1,2 (1) p = -1 , q = -2 (2) p =-1 , q =2 (3) p=1 , q = -2 (4) None of these

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0

If (x)/((x-1)(x^(2)+1)^(2))=(P)/(x-1)+(Qx+R)/(x^(2)+1)+(Sx+T)/((x^(2)+1)^(2)) , then P+Q-R-S+T= ____________.

If one root of the equation qx^(2)+px+q=0p,q being real) be imaginary,show that the roots of the equation x^(2)-4qx+p^(2)= 0are real and unequal