If the roots of the equation `(a^(2)+^(2))x^(2)-2(ac+bd)x+(c^(2)+d^(2))=0` are equal , prove that `(a)/(b)=(c )/(d)`

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

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

The roots of the quadratic equation (a + b-2c)x^2- (2a-b-c) x + (a-2b + c) = 0 are

State the roots of quadratic equation ax^(2)+bx+c=0" if "b^(2)-4ac gt0

a,b,c,d are in G.P. Prove that a^(2)-b^(2),b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

If m_(1) and m_(2) are the roots of the equation x^(2) + ( sqrt(3) + 2) x + sqrt(3) - 1 =0 then prove that area of the triangle formed by the lines y=m_(1) x, y=m_(2) x and y=c is (c^2)/( 4) ( sqrt(33) + sqrt(11)) .

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)

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If a,b,c and d are the roots of the equation x^(4)+2x^(3)+4x^(2)+8x+16=0 the value of the determinant |{:(1+a,1,1,1),(1,1+b,1,1),(1,1,1+c,1),(1,1,1,1+d):}| is

The number of solution of the set of equations (x^(2))/a^(2)+(y^(2))/(b^(2))-(z^(2))/(c^(2))=0,(x^(2))/(a^(2))-(y^(2))/(b^(2))+(z^(2))/(c^(2))=0,-(x^(2))/(a^(2))+(y^(2))/(b^(2))+(z^(2))/(c^(2))=0 is