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If $$x_1$$ and $$x_2$$ are the roots of the equation $$x^{2} - 4x - c = 0$$ and $$5x_1 - x_2 = 38$$, which of the following statements is true?
Using the sum of roots:
$$x_1+x_2=4$$
Given,
$$5x_1-x_2=38$$
Substituting the value of $$x_2$$ from the first equation into the given condition:
$$5x_1-(4-x_1)=38$$
$$6x_1=42 \Rightarrow x_1=7$$
Therefore,
$$x_2=4-7=-3$$
Using the product of roots:
$$x_1x_2=-c$$
$$7\times(-3)=-c$$
$$c=21$$
Correct Answer: Option A.
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