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Solving a Quadratic Equation by Completion of Squares Method

If x=3 is o...

Question

If $x = 3$ is one root of the equation $k x^{2} - 10 x + 3 = 0$ , find the value of $k$ .

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Solution

Given,

$x = 3$ is one root of the equation $k x^{2} - 10 x + 3 = 0$

implies that, the root should satisfy the equation

$k (3)^{2} - 10 (3) + 3 = 0$

$9 k - 30 + 3 = 0$

$9 k = 27$

$∴ k = 3$

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