If the quadratic equations 3x2−7x+2=0 and kx2+7x−3=0 has a common root then the positive value of k is ____

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If the quadratic equations $3 x^{2} - 7 x + 2 = 0$ and $k x^{2} + 7 x - 3 = 0$ has a common root then the positive value of k is _____

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answer is 6.

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Detailed Solution

$3 x^{2} - 7 x + 12 = 0 \Rightarrow 3 x^{2} - 6 x - x + 2 = 0 \Rightarrow 3 x (x - 2) - 1 (x - 2) = 0 \Rightarrow (3 x - 1) (x - 2) = 0$
$\Rightarrow x = 2 o r x = 1 / 3$
If x=2 is a common root, then 2 lies on
$k x^{2} + 7 x - 3 = 0 \Rightarrow 4 k + 14 - 3 = 0 \Rightarrow 4 k + 11 = 0$

$\Rightarrow k = - 11 / 4$
If $x = \frac{1}{3}$ is a common root, then $\frac{1}{3}$ lies on
$k x^{2} + 7 x - 3 = 0 \Rightarrow \frac{k}{9} + \frac{7}{3} - 3 = 0 \Rightarrow k + 21 - 27 = 0$
$\Rightarrow k = 6$