Question

If one root of the quadratic equation kx² – 20x + 34 = 0 is $5-2\sqrt{2}$, find k.

Answer 1

Given: kx² – 20x + 34 = 0

On comparing this equation with ax² + bx + c = 0, we get:

a = k, b = –20 and c = 34
$\mathrm{Let}\alpha =5-2\sqrt{2},\mathrm{Then},\beta =5+2\sqrt{2}$

Thus,
$\alpha +\beta =5-2\sqrt{2}+5+2\sqrt{2}=10$

We know that

$$\begin{gathered} \alpha +\beta =\frac{-b}{a} \\ \mathrm{So},\frac{-b}{a}=10 \end{gathered}$$

Since, a = k and b = –20, we get:
$$\begin{gathered} -\frac{-20}{k}=10 \\ \Rightarrow k=\frac{20}{10}=2 \end{gathered}$$