Discriminant Related Question [SOLVED] Discriminant Related Question

[_Mayday_]

[SOLVED] Discriminant Related Question

Question

$$x^2 - 8x - 29 = (x+a)^2 +b$$, where a and b are constant.

NOTE: The equals sign should be an always equals sign, so like three lines under each other

(a) Find the value of a and b

(b)Hence, or otherwise show the roots of $$x^2 - 8x - 29 = 0$$ are $$c =+/- d\sqrt5$$ where c and d are integers.

Attempt

(a)$$x^2 - 8x - 29 = (x+a)^2 +b$$

$$(x-4)^2 - 16 - 29 = (x+a)^2 +b$$

a = -4
b = -45

(b) Erm...not sure, as it says roots I will assume it means two roots so $$b^2 - 4ac > 0$$

64 + 116 > 0, yes this is all alright but I am not sure how to get it in the form $$c =+/- d\sqrt5$$

_Mayday_

 

[DavidWhitbeck]

NOTE: The equals sign should be an always equals sign, so like three lines under each other

Oh that's done with \equiv

$$\equiv$$

 

[_Mayday_]

Oh that's done with \equiv

$$\equiv$$

Cheers!

Anyone got any ideas on how to solve the other question? :rofl:

 

[HallsofIvy]

What are the roots of the equation x²- 8x- 29= 0? Since you have already "completed the square" that should be easy!

 

[_Mayday_]

By find the roots do they just mean find the possible values for x? The question is what has got me, what do they mean by find the roots? I know I should know this but, I think I have already done the 'hard' bit.

 

[_Mayday_]

$$(x-4)^2 = 45$$

$$\sqrt{45} = +/- 3\sqrt5$$

 

[_Mayday_]

$$x - 4 = +\- 3\sqrt5$$

$$x = 4 +/- 3\sqrt5$$

 

[_Mayday_]

I think that is correct, thank you!