If `a x^2+b x+c=0 and b x^2+c x+a=0` have a common root and a, b, and c are nonzero real numbers, then find the value of `(a^3+b^3+c^3)//a b c`

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

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+ c dot

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

Let a, b, c be real numbers such that ax^(2) + bx + c = 0 and x^(2) + x + 1 = 0 have a common root. Statement-1: a = b = c Staement-2: Two quadratic equations with real coefficients cannot have only one imainary root common.

If x^(2)+bx+c=0, x^(2)+cx+b=0 (b ne c) have a common root, then show that b+c+1=0

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roots, then a. a=b=c b. a=b!=c c. a=-b=c d. none of these.