Question

If -1/2 is a root of the equation ^2+5 + 2 = 0, find .

Answer 1

Given:

-1/2 is a root of the following equation:

$^2+5+2=0$

First, we will find the value of k

substitute with a = -1/2

so,

$\begin{gathered} k\cdot(-\frac{1}{2})^2+5\cdot(-\frac{1}{2})+2=0 \\ k\cdot\frac{1}{4}-\frac{5}{2}+2=0 \\ k\cdot\frac{1}{4}-\frac{1}{2}=0 \\ k\cdot\frac{1}{4}=\frac{1}{2} \\ k=2 \end{gathered}$

So, the equation will be:

$2^2+5+2=0$

Now, factor the equation:

$\begin{gathered} (2a+1)(a+2)=0 \\ 2a+1=0\rightarrow a=-\frac{1}{2} \\ or,a+2=0\rightarrow a=-2 \end{gathered}$

So, the answer will be:

$a=\mleft\lbrace-2,-\frac{1}{2}\mright\rbrace$