If `(b^2-4a c)^2(1+4a^2)<64 a^2, a<0` , then maximum value of quadratic expression `a x^2+b x+c` is always less than a. 0 b. 2 c. -1 d. -2

The value of c for which the equation a x^2+2b x+c=0 has equal roots is (b^2)/a (b) (b^2)/(4a) (c) (a^2)/b (d) (a^2)/(4b)

If a^(2)+b^(2)+c^(2)=1 where, a,b, cin R , then the maximum value of (4a-3b)^(2) + (5b-4c)^(2)+(3c-5a)^(2) is

If a^(2) + b^(2) + c^(2) = 2(a-b-c)-3 , then the value of 4a - 3b + 5c is

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

If ((a^(2)+1)^(2))/(2a-i)=x=iy, then x^(2)+y^(2) is equal to ((a^(2)+1)^(4))/(4a^(2)+1) b.((a+1)^(2))/(4a^(2)+1) c.((a^(2)-1)^(2))/((4a^(2)-1)^(2)) d.none of these

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))

If a + b + c = 0 , prove that a^(4) + b^(4) + c^(4) = 2(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) = 1//2 (a^(2) + b^(2) + c^(2))^(2)

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2