Multiple choice

If the equation $x^2+ax+bc=0$ and $x^2+bx+ca=0$ have one common root, then their remaining roots are-

  1. $1,b$
  2. $b,a$
  3. $b,c$
  4. $c,a$
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B Correct answer
Explanation

Let alpha be the common root. alpha^2 + a*alpha + bc = 0 and alpha^2 + b*alpha + ca = 0. Subtracting: (a-b)*alpha + c(b-a) = 0 => (a-b)*alpha = c(a-b). If a != b, alpha = c. Substituting c into the first: c^2 + ac + bc = 0 => c(c+a+b) = 0. The roots of the first are c and b. The roots of the second are c and a.

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