Question

# The value of $k$ for which $3$ is a root of the equation $k{x^2} - 7x + 3 = 0$ is(A) $2$(B) $- 2$(C) $3$(D) $- 3$

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Hint:To solve this type of problem we have to have knowledge of quadratic equation systems. Whenever a question say $\alpha$ is one of the roots of $a{x^2} + bx + c = 0$ then in this case we substitute $x = \alpha$ in the given equation. So that we can find any variable that is used in the equation but value is not assigned.

Here we have an equation $k{x^2} - 7x + 3 = 0$ and root of this equation is $3$
So to find the value of $k$ substitute $x = 3$ in above equation
Then, $k \times {\left( 3 \right)^2} - 7 \times 3 + 3 = 0$
From this we get
$9k - 21 + 3 = 0$
Further solving this we get
$9k - 18 = 0$
Now separate variable and constant term to find value of $k$
$9k = 18$
From here $k = \dfrac{{18}}{9}$
After solving the above equation we get $k = 2$

So, the correct answer is “Option A”.

Note:A quadratic equation $f(x) =$$a{x^2} + bx + c$ having two roots are $\alpha$ and $\beta$ then $f(\alpha )$ and $f(\beta )$ are always equals to zero. And this rule can also be valid for any expression.