Let `x^2-px+q=0,` where `p in R,q in R` have the roots `alpha,beta` such that `alpha+2beta=0` then - (i) `2p^2+q=0` (ii) `2q^2+p=0` (iii)`qlt0` (iv) none of these

Let x^(2)-px+q=0, where p in R,q in R have the roots alpha,beta such that alpha+2 beta=0 then -(i)2p^(2)+q=0 (ii) 2q^(2)+p=0( iii) q<0 (iv) none of these

If (alpha)/(beta) and (beta)/(alpha) are the real roots of px^(2)+qx+r=0 then (A)p=r(B)q^(2)=pq (C) q^(2)=2pr(D) none of these

If 3 - 4i is a root of x^(2) - px + q = 0 where p, q in R . then value (2 p - q)/( p + q) is

If all the equations x^(2)+px+10,x^(2)+qx+8=0 and x^(2)+(2p+3q)x+60=0 where p,q in R have a common root,then the value of (p-q) can be (i) -1( ii) 0( iii) 1 (iv) 2

If tan alpha, tan beta are the roots of the equation x^(2)+px+q=0(p!=0), then (i) sin(alpha+beta)=-p( ii) tan(alpha+beta)=(p)/(q-1) (iii) cos(alpha+beta)=(1-q)( iv) none of these

If tan alpha, tan beta are the roots of the equation x^(2)+px+q=0,(p!=0), then (i) sin(alpha+beta)=-p( ii) tan(alpha+beta)=(p)/(q-1) (iii) cos(alpha+beta)=(1-q)( iv) 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 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

Consider the quadratic polynomial 'f(x)=x^(2)-px+q' where 'f(x)=0' has prime roots alpha and beta and 'p=alpha+beta' , 'q=alpha beta' .If 'p+q=11' and 'a=p^(2)+q^(2)' then find the value of 'f(a)/100' where a is an odd positive integer.

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)