If `A=[(a,b),(c,d)]" "("where "bc ne 0)` satifies the equations `x^(2)+k=0`, then

If A=[a b c d] (where b c!=0 ) satisfies the equations x^2+k=0,t h e n a+d=0 b. K=-|A| c. k=|A| d. none of these

Consider, A=[(a,2,1),(0,b,0),(0,-3,c)] , where a, b and c are the roots of the equation x^(3)-3x^(2)+2x-1=0 . If matric B is such that AB=BA, A+B-2I ne O and A^(2)-B^(2)=4I-4B , then find the value of det. (B)

If alpha" and "beta are the roots of the equation ax^(2)+bx+c=0, (c ne 0) , then the equation whose roots are (1)/(a alpha +b)" and "(1)/(a beta +b) is

If a,b,c,d in R-{0} , such that a,b are the roots of equation x^(2)+cx+d=0 and c,d are the roots of equation x^(2)+ax+b=0, then |a|+|b|+|c|+|d| is equal to

In a triangle A B C ,/_C=pi/2dot If tan(A/2) and tan(B/2) are the roots of the equation a x^2+b x+c=0,(a!=0), then the value of (a+b)/c (where a , b , c , are sides of opposite to angles A , B , C , respectively) is

If a and b are the roots of the equation x^(2)+ax+b=0, a ne 0, b ne 0 , then the values of a and b are respectively

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in R

If alphaa n dbeta are the roots of the equation x^2+b c+c=0 ,where cltaltb then a. 0ltalphaltbeta b. alphalt0ltbetalt|alpha| c. alphaltbetalt0 d. alphalt0lt |alpha|ltbeta

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .