If the equation `x^3-x^2+b x+c=0 and x^3+c x^2+b x-d=0` have two commoon roots then show that `b^2 =d.`

If the equation x^(3)-x^(2)+bx+c=0 and x^(3)+cx^(2)+bx-d=0 have two commoon roots then show that b^(2)=d .

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

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.

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) a+b+c=3

If the equations a x^2+b x+c=0a n dx^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

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

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

If the equation x^2+b x-a=0"and" x^2-a x+b=0 have a common root, then a. a+b=0 b. a=b c. a-b=1 d. a+b=1

IF x^2 + a x + bc = 0 and x^2 + b x + c a = 0 have a common root , then a + b+ c=

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