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 this question simply put the value of roots i.e. 2 in the equation $k{x^2} - 14x + 8 = 0$. Use this to find the value of k.

Complete step-by-step answer:
According to the question, $2$ is the one root of the quadratic equation $k{x^2} - 14x + 8 = 0$ is given.
Hence we have to find the value of $k$
$k{x^2} - 14x + 8 = 0$, root is $2$
So,
$
  \Rightarrow k{\left( 2 \right)^2} - 14 \times 2 + 8 = 0 \\
  \Rightarrow k \times 4 = - 8 + 28 \\
  \Rightarrow k \times 4 = 20 \\
  \Rightarrow k = \dfrac{{20}}{4} \\
  \therefore k = 5 \\
 $

Note: In such types of questions by the concept of quadratic equations used as we know that to find the roots of any quadratic equation we use $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$ formula and hence in the above question the one root is given i.e. the value of $x$ is given so substitute the value in the equation and get the value.