The roots of the equation `ax^(2)+bx+c=0` where `a!=0`,are: 1) `(b+-sqrt(b^(2)-4ac))/(2a),` 2) `(-b+-sqrt(b^(2)-4ac))/(2c),` 3) `(-b+sqrt(b^(2)-4ac))/(2a),` 4) `(2a)/(2a-b+sqrt(b^(2)-4ac)`

If the roots of the equation ax^(2)+bx+c=0 be in the ratio 3:4, show that 12b^(2)=49ac .

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 the roots of the equation ax^2+bx+c=0 be in the ratio m:n, prove that sqrt(m/n)+sqrt(n/m)+b/sqrt(ac)=0

If t a nthetaa n ds e ctheta are the roots of the equation a x^2+b x+c=0 , then |s e ctheta-t a ntheta|=(sqrt(b^2-4a c))/(|a|) b. |s e ctheta-t a ntheta|=(sqrt(b^2+4a c))/(|a|) c. a^4+b^2(-4a c+b^2) d. b^4=a^2(4a c+a^2)

If r is the ratio of the roots of the equation ax^2 + bx + c = 0 , show that (r+1)^2/r =(b^2)/(ac)

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)

the roots of the equation (a+sqrt(b))^(x^2-15)+(a-sqrt(b))^(x^2-15)=2a where a^2-b=1 are

the roots of the equation (a+sqrt(b))^(x^2-15)+(a-sqrt(b))^(x^2-15)=2a where a^2-b=1 are

If alpha and beta are the roots of the equation ax^(2)+bc+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If the roots of the equation ax^(2)+bx+c=0(a!=0) be alpha and beta and those of the equation Ax^(2)+Bx+C=0(A!=0) be alpha+k and beta+k .Prove that (b^(2)-4ac)/(B^(2)-4AC)=(a/A)^(2)