Show that the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal if a,b,c are in H.P.

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

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

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

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0 be equal then prove that a,b,c are in Harmonic progression .

If sectheta+tantheta=1 then one root of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 is

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.