Quadratic EquationHard
Question
The possible values of ' $b$ ', $b \in R$ for which the equations $2017x^{2} + bx + 7102 = 0$ and $7102x^{2} + bx + 2017 = 0$ have a common root is/are
Options
A.-9119
B.-10879
C.9119
D.10879
Solution
Let $\alpha$ be the common root
$$\begin{matrix} \Rightarrow & 2017\alpha^{2} + b\alpha + 7102 & & = 0 \\ \text{~and~} & 7102\alpha^{2} + b\alpha + 2017 & & = 0 \\ \text{~Subtracting,~} & 5085\alpha^{2} - 5085 & & = 0 \\ \Rightarrow & & \alpha & = \pm 1 \end{matrix}$$
Put $\alpha = \pm 1,b = \pm 9119$
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