If x3−6x2+11x−6=0x3−6x2+11x−6=0 and x3+3x2−6x−8=0x3+3x2−6x−8=0 have one common root between them. What is the value of that root?
Choose the correct choice
A) 3	B) 2	C) 6	D) 9	E) 1
There are two equations,   x3−6x2+11x−6=0x3−6x2+11x−6=0 - - - (i)   x3+3x2−6x−8=0x3+3x2−6x−8=0 - - - (ii)   So both (i) and (ii) have one root in common and we know that at the root the value of both the equations is 0. Suppose that common root is x then,   x3−6x2+11x−6x3−6x2+11x−6 = x3+3x2−6x−8x3+3x2−6x−8 ⇒⇒ 9x2−17x−2=09x2−17x−2=0   ⇒⇒ (x - 2)(9x + 1) = 0 or x = 2 or -1/9. As by applying the Descartes rule in (i) we can see it cannot have any negative root so x = 2.   Why are we getting two values x = 2 and x = -1/9?   x = 2 and x = -1/9 are the pint of intersections of these two equations out of which x = 2 is the point of intersection at x axis therefore this point (x = 2) is the common root as well.   Answer:2
<result>B</result>
If x3−6x2+11x−6=0x3−6x2+11x−6=0 and x3+3x2−6x−8=0x3+3x2−6x−8=0 have one common root between them. What is the value of that root?