Question

find all values of k such that x^2-kx+9 = 0 has two imaginary roots

Answer 1

do u know discriminant of this equaation

Answer 2

6

Answer 3

but thats not right apparently

Answer 4

formula for discriminant

\(\large \color{black}{\begin{align} if\quad ax^2+bx+c=0\hspace{.33em}\\~\\
then\quad D=b^2-4ac\hspace{.33em}\\~\\
\end{align}}\)

Answer 5

can u find \(D\) now?

Answer 6

-k^2-36

Answer 7

some fault there ,

note that \(\large b=-k\) here

Answer 8

yeah and i said (-k)^2

Answer 9

\(-k^2\neq (-k)^2\)

Answer 10

\((-k)^2=k^2\)

Answer 11

ok

Answer 12

ok the discriminant property says that the equation has imaginary roots if

\(\large \color{black}{\begin{align} D<0\hspace{.33em}\\~\\
\end{align}}\)

Answer 13

yes

Answer 14

so

\(\large \color{black}{\begin{align} k^2-36<0\hspace{.33em}\\~\\
\end{align}}\)


can u solve this

Answer 15

k< 6

Answer 16

that's not complete,

use the property that

\(\large \color{black}{\begin{align} a^2-b^2=(a-b)(a+b)\hspace{.33em}\\~\\
\end{align}}\)

Answer 17

can you tell me what you got

Answer 18

i got

\(\large \color{black}{\begin{align} k^2-36<0\hspace{.33em}\\~\\
k^2-6^2<0\hspace{.33em}\\~\\
\end{align}}\)

Answer 19

isnt it k> -6

Answer 20

now we have

\(\large \color{black}{\begin{align}
k^2-6^2<0\hspace{.33em}\\~\\
(k-6)(k+6)<0\hspace{.33em}\\~\\
\end{align}}\)

Answer 21

so we have

\(\large \color{black}{\begin{align}

k<6\hspace{.33em}\\~\\
and \hspace{.33em}\\~\\
k>-6\hspace{.33em}\\~\\
\end{align}}\)

Answer 22

so

\(\large \color{black}{\begin{align}

-6<k<6\hspace{.33em}\\~\\
\end{align}}\)