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  4. The equation (x-1)(x-2)(x-3)=24 has the real root equal to ' a ' and the complex roots b and c. Then the value of (b c/a), is

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Q. The equation $(x-1)(x-2)(x-3)=24$ has the real root equal to ' $a$ ' and the complex roots $b$ and $c$. Then the value of $\frac{b c}{a}$, is

Complex Numbers and Quadratic Equations

Solution:

cubic is $x^3-6 x^2+11 x-30=0$
$(x-5)\left(x^2-x+6\right)=0$
Hence $a=5 ; b c=6 \Rightarrow \frac{b c}{a}=\frac{6}{5}$