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,care non zero rational no then prove roots of equation (abc^(2))x^(2)+3a^(2)cx+b^(2)cx-6a^(2)-ab+2b^(2)=0 are rational.

If a,b,c,d are rational and are in G.P. then the rooots of equation (a-c)^2 x^2+(b-c)^2x+(b-x)^2-(a-d)^2= are necessarily (A) imaginary (B) irrational (C) rational (D) real and equal

a,b,c are rational.Then the roots of (a+b+c)x^(2)2(a+c)x+(a-b+c)=0 are.

If the roots of the equation x^(2)+2cx+ab=0 are real and unequal,then the roots of the equation x^(2)-2(a+b)x+(a^(2)+b^(2)+2c^(2))=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

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 rational numbers a,b,c be th pth, qth, rth terms respectively of an A.P. then roots of the equation a(q-r)x^2+b(r-p)x+c(p-q)=0 are necessarily (A) imaginary (B) rational (C) irrational (D) real and equal

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are,when ab+bc+ca=0