First slide

Theory of equations

Question

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

Moderate

A

$\sqrt{abc}$
B

$2 \sqrt{abc}$
C

$\sqrt{ab + bc + ca}$
D

$2 \sqrt{ab + bc + ca}$

Solution

Let the roots be $α, β, β, γ$ and $γ, α$ then,
$\begin{aligned} αβ = b, βγ = c and γα = a \\ \Rightarrow αβγ = \sqrt{abc} \end{aligned}$

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