Question

If 2x2-(2+k)x+k=0 where K is a real number, find the roots of the equation

Answer 1

let the k=1
2*2-(2+1)x+1=0
4-3x+1=0
-3x+5=0
3x=5
x=5/3

Answer 2

Answer:

The two roots of the equation are 1 and $\frac{k}{2}$.

Step-by-step explanation:

The given equation is

$2x^2-(2+k)x+k=0$

Quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Using quadratic formula, the roots of given equation are

$x=\frac{-[-(2+k)]\pm\sqrt{[-(2+k)]^2-4(2)(k)}}{2(2)}$

$x=\frac{(2+k)\pm\sqrt{4+4k+k^2-8k}}{4}$

$x=\frac{(2+k)\pm\sqrt{4-4k+k^2}}{4}$

$x=\frac{(2+k)\pm\sqrt{(k-2)^2}}{4}$

$x=\frac{(2+k)\pm(k-2)}{4}$

If we consider positive sign,

$x=\frac{(2+k)+(k-2)}{4}$

$x=\frac{2k}{4}=\frac{k}{2}$

If we consider negative sign,

$x=\frac{(2+k)-(k-2)}{4}$

$x=\frac{2+k-k+2}{4}$

$x=\frac{4}{4}=1$

Therefore the two roots of the equation are 1 and $\frac{k}{2}$.