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Question
If one root of the equation \[x^2 + px + 12 = 0\] while the equation \[x^2 + px + q = 0\] has equal roots, the value of q is
Options
49/4
4/49
4
none of these
Solution
49/4
It is given that, 4 is the root of the equation \[x^2 + px + 12 = 0\].
\[\therefore 16 + 4p + 12 = 0\]
\[ \Rightarrow p = - 7\]
It is also given that, the equation
\[\therefore p^2 - 4q = 0\]
\[ \Rightarrow 4q = \left( - 7 \right)^2 = 49\]
\[ \Rightarrow q = \frac{49}{4}\]
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