The equation `[1x y][1 3 4 0 2-1 0 0 1]=[0]` has fo`ry=0` b. rational roots for `y=-1` d. integral roots Then (ii) a. (p) (r) b. (q) (p) c. (p) (q) d. (r) (p)

If p,q,r in R and the quadratic equation px^2+qx+r=0 has no real roots, then (A) p(p+q+r)gt0 (B) (p+q+r)gt0 (C) q(p+q+r)gt0 (D) p+q+rgt0

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, x^3 + px^2+qx-1 = 0 form an increasing G.P. where p and q are real,then (a) p +q = 0 (b) p in (-3, oo) (c) one of the roots is unity (d) one root is smaller than 1 and one root is greater than 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

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these

The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), and (r q ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are (1,2) (b) (2,-1) (c) (1,-1) (d) (2,3)

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. 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

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 , a x+(q+b)y+c z=0 , a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is a. -1 b. 0 c. 1 d. 2