If equations $x^{2} - k x - 21 = 0$ and $x^{2} - 3 k x + 35 = 0; k > 0$ have a common root, then k is equal to:

-4

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-4 or 4

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Solution

The correct option is D 4
Soln: The equations $x^{2} - k x - 21 = 0$ and $x^{2} - 3 k x + 35 = 0$ have a common root.

So, equating the two equations:

$x^{2} - k x - 21 = x^{2} - 3 k x + 35$

$2 k x = 56$

$k = \frac{28}{x}$

Putting in the equation:

$x^{2} - 28 - 21 = 0$

$x^{2} = 49$

$x = + 7$

$o r k = + 4, A s, k > 0, k = 4.$ Hence option (d)

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