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(-(1)/(2))^2+5\cdot(-(1)/(2))+2=0 \\ k\cdot(1)/(4)-(5)/(2)+2=0 \\ k\cdot(1)/(4)-(1)/(2)=0 \\ k\cdot(1)/(4)=(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=-(1)/(2) \\ or,a+2=0\rightarrow a=-2 \end{gathered}`

So, the answer will be:

`a=\mleft\lbrace-2,-(1)/(2)\mright\rbrace`