If `a,b,c` are in GP, show that the equations `ax^(2)+2bx+c=0` and `dx^(2)+2ex+f=0` have a common root if `a/d,b/e,c/f` are in HP

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have one root in common is

If a,b, c epsilon R(a!=0) and a+2b+4c=0 then equatio ax^(2)+bx+c=0 has

If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c^(2)+d^(2) are also in G.P.

If ax^2 + bx + c = 0 and bx^2 + cx+a= 0 have a common root and a!=0 then (a^3+b^3+c^3)/(abc) is

If each pair of the three equations x^(2)+ax+b=0, x^(2)+cx+d=0 and x^(2)+ex+f=0 has exactly one root in common then show that (a+c+e)^(2)=4(ac+ce+ea-b-d-f)

If the quadratic equations, a x^2+2c x+b=0 and a x^2+2b x+c=0(b!=c) have a common root, then a+4b+4c is equal to:

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

The equation ax^(2) +bx+ c=0, where a,b,c are the side of a DeltaABC, and the equation x^(2) +sqrt2x+1=0 have a common root. Find measure for angle C.