[Fudge Cream]

Okay so two questions:

x^2 + 2x + 3 is the equation given.

1) Find the value of the discriminant of x^2 + 2x + 3. Explain how the sign of the discriminant relates to your graph sketch (previous questions)

Okay so I found out the discriminant (i think), which is 2^2 - (4*3*1) = -8.

So how does this relate to my graph?

2) The equation x^2 + kx + 3= 0, where k is a constant, has no real roots. Find the set of possible values of k, giving your answer in surd form.

I have no idea of how to start that question.

Please help, thanks
Fudge

[nuodai]

The discriminant tells you how many roots the equation has. Namely,
(a) If b²-4ac < 0, then the equation has no real roots; or
(b) If b²-4ac = 0, then the equation has one repeated real root; or
(c) If b²-4ac > 0, then the equation has two real roots

Now, if y = f(x), then a "root" occurs when the curve crosses the x-axis (when y=0), so f(x) = 0. This means that, if there are no real roots, the curve doesn't cross the x-axis; if there is a repeated root, it only touches the x-axis; and if there are two roots, it crosses the x-axis in two places.

This pretty much answers (1) for you. You can use it to answer (2) by finding a condition on the discriminant (in terms of k) for which the equation has no real roots.

[Fudge Cream]

^^^ ah thank you both, Noudai i've just started as maths, so i still don't get how to do the constant question.

[Revolution is my Name]

Originally Posted by Fudge Cream

^^^ ah thank you both, Noudai i've just started as maths, so i still don't get how to do the constant question.

You just need to sub in the values given (including K) into the discriminant (which you set to equal less than 0), then simplify