Quadratic EquationHard

Question

Given that the equation $(x - 19)(x - 97) = p$ has real roots $\alpha$ and $\beta$. Then the minimum real root of the equation $(x - \alpha)(x - \beta) = - p$ is

Options

A.13
B.16
C.18
D.19

Solution

$(x - 19)(x - 97) - p = (x - \alpha)(x - \beta)$

$$\Rightarrow \ (x - \alpha)(x - \beta) + p = (x - 19)(x - 97)$$

$\Rightarrow \ $ Roots of $(x - \alpha)(x - \beta) = - P$ are 19 and 97

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