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# Further Maths Help watch

1. How would I answer this:

The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

This is FP1, exam board: Edexcel.
2. (Original post by Doctor1234)

The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

This is FP1, exam board: Edexcel.
If the quadratic in z doesn't have real roots, what do you know about the discriminant? (from C1)
3. (Original post by Doctor1234)

The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

This is FP1, exam board: Edexcel.
Well, it's a quadratic with real coefficients. What's the condition on the discriminant that would imply complex roots for this equation?
4. Erm, we haven't covered discrimants yet.
5. (Original post by Doctor1234)
Erm, we haven't covered discrimants yet.
Should be like one of the first things in C1... maybe even at GCSE.

The discriminant of a quadratic where is given by .

Certain conditions on it determine the amount of real roots that the equation has.
6. (Original post by Doctor1234)
Erm, we haven't covered discrimants yet.
Okay, so I suppose you know the quadratic formula from GCSE:

.

Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.

We call the bit inside the square root, ie the discriminant.

Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
7. (Original post by K-Man_PhysCheM)
Okay, so I suppose you know the quadratic formula from GCSE:

.

Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.

We call the bit inside the square root, ie the discriminant.

Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
b^2 has to be less than 44 to obtain a non-real complex number?
8. (Original post by Doctor1234)
b^2 has to be less than 44 to obtain a non-real complex number?
Yes, so what range must lie between?

(Hint: sketch the parabola and look for the range of values where the curve lies below the line . This will be a common technique for solving quadratic inequalities in A-level maths /FM)
9. (Original post by K-Man_PhysCheM)
Yes, so what range must lie between?

(Hint: sketch the parabola and look for the range of values where the curve lies below the line . This will be a common technique for solving quadratic inequalities in A-level maths /FM)
As long as y is greater than 0 and less than 44?
10. (Original post by Doctor1234)
As long as y is greater than 0 and less than 44?
No, you need to sketch the parabola.

Then sketching and shows me that the curve is underneath the line between -2 and 2. So in this case, .

Use the same for your question.
Attached Images

11. So in my case the curve would be underneath the line + or - root 44?
12. (Original post by Doctor1234)
So in my case the curve would be underneath the line + or - root 44?
Yeah, and that surd can be simplified and should be written as an inequality with b.
13. (Original post by RDKGames)
Should be like one of the first things in C1... maybe even at GCSE.

The discriminant of a quadratic where is given by .

Certain conditions on it determine the amount of real roots that the equation has.
Why do you use notation the OP probably won't understand?
14. (Original post by Ano9901whichone)
Why do you use notation the OP probably won't understand?
This notation is completely fine for FP1, there’s nothing OP should be unfamiliar with here
15. (Original post by K-Man_PhysCheM)
Yeah, and that surd can be simplified and should be written as an inequality with b.
I see, it makes sense. So it b is out of the range -(sqrt 44) and +(sqrt 44), then the equation would have real roots rather than imaginary roots?
16. (Original post by Protostar)
This notation is completely fine for FP1, there’s nothing OP should be unfamiliar with here
It looks a bit different than how I would format it on paper but yeah you need set notation for the things like solving sets of equations.
17. (Original post by Doctor1234)
I see, it makes sense. So it b is out of the range -(sqrt 44) and +(sqrt 44), then the equation would have real roots rather than imaginary roots?
Yes, that is right.

Note it should be

and NOT

because when is exactly on the boundary, the quadratic would have one real repeated root.

PS: it's good practice to always fully simplify surds
18. (Original post by K-Man_PhysCheM)
Yes, that is right.

Note it should be

and NOT

because when is exactly on the boundary, the quadratic would have one real repeated root.

PS: it's good practice to always fully simplify surds
Thanks for the help, cleared a lot of confusion. Are you doing A levels or are you at uni?
19. (Original post by Doctor1234)
Thanks for the help, cleared a lot of confusion. Are you doing A levels or are you at uni?
No worries

I'm in Year 13, so not at Uni yet!
20. (Original post by K-Man_PhysCheM)
No worries

I'm in Year 13, so not at Uni yet!
Oh kl, well good luck with A2.

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