Question

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

Answer 1

Step 1. Find the value of $k$ in the quadratic equation

The quadratic equation$k{x}^2-14x+8=0$

We need to find the value of $k$

Let the value of $x=2$

$$\begin{gathered} \therefore k\left(2^2\right)–14\left(2\right)+8=0 \\ \Rightarrow 4k–28+8=0 \\ \Rightarrow 4k-20=0 \\ \Rightarrow 4k=20 \\ \Rightarrow k=\frac{20}{4} \\ \Rightarrow k=5 \end{gathered}$$

Step 2. Checking the value of $k$

$$\begin{gathered} \therefore 5\left(2^2\right)–14\left(2\right)+8 \\ =20–28+8 \\ =20–20 \\ =0 \end{gathered}$$

Hence the value of $k$ for which the quadratic equation $k{x}^2-14x+8=0$ is $5$.