If `a, b, c, d >0, x in R` and `(a^2+b^2+c^2)x^2-2(ab+bc+cd)x+b^2+c^2+d^2<=0` then, `|[1,1,loga],[1,2,logb],[1,3,logc]|=`

If a,b,c,d gt 0 , x in R and (a^(2)+b^(2)+c^(2))x^(2)-2(ab+bc+cd)x+b^(2)+c^(2)+d^(2) le 0 , then |{:(33,14,loga),(65,27,logb),(97,40,logc):}|=

If a,b,c,d,e,x are real and (a^2+b^2+c^2+d^2)x^2-2(ab+bc+cd+de)x+(b^2+c^2+d^2+e^2)le0 then a,b,c,d,e are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c,d, x are real and the roots of equation (a^2+b^2+c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2)=0 are real and equal then a,b,c,d are in (A) A.P (B) G.P. (C) H.P. (D) none of these

If a, b, c and d are in G.P. show that (a ^ 2 +b ^ 2 +c^ 2 )(b^ 2 +c^ 2 +d^ 2 )=(ab+bc+cd)^ 2

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= (a) a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

If a, b, c ,d be in G.P. , show that (i) (b -c)^(2) + (c - a)^(2) +(d -b)^(2) = (a - d)^(2) (ii) a^(2) + b^(2) + c^(2) , ab + bc + cd , b^(2) + c^(2) + d^(2) are in G.P.

If the roots of the equation (a^2+b^2)x^2-2(a c+b d)x+(c^2+d^2)=0 are equal, prove that a/b=c/d

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Factorise : ab (c^2 + d^2) - a^(2) cd - b^(2) cd

Factorise: a^(2) + b^(2) -c^(2)-d^(2)+2ab -2cd