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# Rational Ineq. #2

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Let $$a$$ and $$b$$ be constants. Suppose that the equation

$$\frac{(x+a)(x+b)(x+12)}{(x+3)^2} = 0$$

has exactly $$3$$ distinct roots, while the equation

$$\frac{(x+2a)(x+3)(x+6)}{(x+b)(x+12)} = 0$$

has exactly $$1$$ distinct root. Compute  $$100a+b$$.

Nov 23, 2019