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If $x^{2} - 3 a x + 14 = 0$ and $x^{2} + 2 a x - 16 = 0$ have a common root then $a^{4} + a^{2} =$

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Detailed Solution

${(c_{1} a_{2} - c_{2} a_{1})}^{2} = (a_{1} b_{2} - a_{2} b_{1}) (b_{1} c_{2} - b_{2} c_{1})$

$\Rightarrow a^{2} + a^{4} = 90$

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