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If one of roots of x2 + ax + 4 = 0 is twice the other root, then the value of ‘a’ isA) 8√2 B) √2 C) -3√2 D) -2√2 |
Answer» Correct option is (C) -3√2 Let \(\alpha\;and\;2\alpha\) are roots of \(x^2+ax + 4 = 0\) _______________(1) \(\therefore\) Product of roots = 4 \(\Rightarrow\) \(2\alpha^2=4\) \(\Rightarrow\) \(\alpha^2=2\) \(\Rightarrow\) \(\alpha=\pm\sqrt2\) ______________(2) And sum of roots = -a \(\therefore\) \(-a=\alpha+2\alpha\) \(=3\alpha\) \(=3(\pm\sqrt2)\) (From (2)) \(=\pm3\sqrt2\) \(\therefore a=\mp3\sqrt2\) Possible values of a are \(3\sqrt{2}\;or\;-3\sqrt{2}.\) Correct option is C) -3√2 |
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