If each pair of the equation $x^{2} + ax + b = 0,\ x^{2} + bx + c = 0\ and\ x^{2} + cx + a = 0$ has a common root, then product of all common roots is

Question

Dr. Abubacker · Accepted Answer

(a)
Let the roots be $\alpha,\ \beta,\beta,\ \gamma\ and\ \gamma,\ \alpha,$ then
$\alpha\beta = b,\ \beta\gamma = c\ and\ \gamma\alpha = a$
$\Rightarrow \ \alpha\beta\gamma = \sqrt{abc}$

Q. If each pair of the equation $x^{2} + ax + b = 0,\ x^{2} + bx + c = 0\ and\ x^{2} + cx + a = 0$ has a common root, then product of all common roots is

Explanation

Reviewed by Dr. Abubacker

Want more practice?