Cie a level math p1 help

Can someone please tell me how to determine in which direction to put the inequality at ? I got the answer of K=6 and k=-6
I just don’t know how to put the inequality
Eg>-6 k>6 or etc I just don’t know how to put them ?
The attached image for the question is below , any help would be great . Thank you ..

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OK so you require that the discriminant follows $k^2 - 36 \leq 0$.

So it's the inequality there $k$ is between -6 and 6.

If you're not sure why, then sketch the quadratic $k^2 - 36$ and look for which $k$ values it's equal to 0 or less. Clearly these are the k values between the roots of the equation.

Why did you write k^2-36 <or equal to 0
Isn’t k^2-36 >or equal to 0 ? I don’t understand

Look $f(x) = x^2+kx+9$ is a quadratic, and you want its range to be $f(x) \geq 0$. This means the quadratic either touches the x-axis or is entirely above it, also equivalent to saying it either has equal roots or it has no roots. And that's equivalent to making the discriminant $\leq 0$.