If `a ,b ,c(a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0` ares rational.

If a,b,c are rational then roots of equation abc^2x^2+3a^2 cx+b^2 cx-6a^2-ab+2b^2=0 are (A) irrational (B) rational (C) imaginary (D) irrational if a^2ltb

If a,b,c in Q, then roots of ax^(2)+2(a+b)x-(3a+2b)=0 are rational.

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, a n dC=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

if the roots of (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal then a,b,c are in

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

If a , b , c are real numbers, then find the intervals in which f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2| is increasing or decreasing.

If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot

If a,b,c are rational numbers (a gt b gt c gt 0) and quadratic equation (a+b-2c) x ^(2) + (b+c-2a) x+ (c+a-2b)=0 has a root in the interval (-1,0) then which of the following statement (s) is/are correct ?

If a+b+c=0 and a,b,c are ratiional. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.

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