Find the range of values of k for which the equation x^2 - kx + (k+3) = 0 has no real

b^2 is negative rather than positive (check the original quadratic).

For no real roots $b^2-4ac<0$

b^2 is negative rather than positive (check the original quadratic).

b is negative (-k), but b^2 is positive (-k)^2 = k^2

Thanks for the reply

b is -k

b^2 is (-k)^2, which is k^2

Am I missing something?

Find the range of values of k for which the equation x^2 - kx + (k+3) = 0 has no real roots.

Could I have some help with this question please?

I have got this far:

b^2 - 4ac < 0

k^2 - (4 x 1 x (k+3)) < 0

k^2 - 4k +12 = 0

(k - 6) (k + 2) = 0

k = 6 or k = -2

Afterwards I attempted to draw a graph of k^2 - 4k +12 = 0, however it does not cross the x-axis? Firstly, how is it possible to find solutions to an equation that does not cross the x-axis?

I was going to shade in the areas on the below the x-axis, as this would've given me values for where the equation is less than 0, but it doesn't cross the x-axis?

How should I proceed? Thanks for any help!

That's what I meant - I probably should have been clearer..



Your actual equation would be -k^2 - 4k - 12, which suggests what about the shape of the curve?

The equation is B^2 - 4AC < 0
Where B = (-k)
=> k^2 - 4(k+3) < 0

There should still be no negative sign before the k^2

The curve is a "U" shaped parabola, not an "n" shaped one.*

Okay, I understand. But surely then the second equation will have no solutions?

OP, check the y-intercept in the second equation..

Thanks of your help

Y intercept is 12

Is this incorrect?

Find the range of values of k for which the equation x^2 - kx + (k+3) = 0 has no real roots.

Could I have some help with this question please?

I have got this far:

b^2 - 4ac < 0

k^2 - (4 x 1 x (k+3)) < 0

k^2 - 4k +12 = 0

(k - 6) (k + 2) = 0

k = 6 or k = -2

Afterwards I attempted to draw a graph of k^2 - 4k + 12 = 0, however it does not cross the x-axis? Firstly, how is it possible to find solutions to an equation that does not cross the x-axis?

I was going to shade in the areas on the below the x-axis, as this would've given me values for where the equation is less than 0, but it doesn't cross the x-axis?

How should I proceed? Thanks for any help!