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

If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,beta+delta are the roots of A x^2+B x+C=0,(A!=0) for some constant delta then prove that (b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)

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

If alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of (aalpha^2+c)/(aalpha+b)+(abeta^2+c)/(abeta+b) is a. (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

Simplify: -1/2a^2b^2c+1/3a b^2c-1/4a b c^2-1/5c b^2a^2+1/6c b^2a-1/7c^2a b+1/8c a^2bdot

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+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((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

Simplify: a^2b(a-b^2)+a b^2(4a b-2a^2)-a^3b(1-2b)

if alpha , beta are root of ax^2+bx+c=0 then (1/alpha^2+1/beta^2)^2 (a) (b^(2)(b^(2)-4ac))/(c^(2)a^(2)) (b) (b^(2)(b^(2)-4ac))/(ca^(3)) (c) (b^(2)(b^(2)-4ac))/(a^(4)) (d) (b^(2)-2ac)^2/(c^(4))

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If a x^2+b x+c=0 has equal roots, then c= (a) b/(2a) (b) b/(2a) (c) (-b^2)/(4a) (d) (b^2)/(4a)