Question

Find the value of k for which one root of the quadratic equation $$k{x^2} - 14x + 8 = 0$$ is $$2$$ .

Answer 1

Hint: In the question, the quadratic equation is given which one unknown value, also the root is given, to get the value of k we need put the root value which is 2 in the place of x so that we will get the value of k.

Complete step-by-step answer:
Given that 2 is a root of equation
So, it must satisfy the equation
Putting $$x = 2$$ in the equation

$\Rightarrow$ $k{x^2} - 14x + 8$ = 0
$\Rightarrow$ $k{(2)^2} - 14(2) + 8$ = 0
$\Rightarrow$ $k \times 4 - 28 + 8$ = 0
$\Rightarrow$ $4k = 28 - 8$ = 20
$\Rightarrow$ k = $\dfrac{{20}}{4} $
$$k = 5$$
Hence the value of k for which one root of the quadratic equation $$k{x^2} - 14x + 8 = 0$$ is $$2$$ is 5.

Note: Here one root is already given. So put the value in the quadratic equation to get another root value. The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation.