# Discriminant Related Question

[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_

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NOTE: The equals sign should be an always equals sign, so like three lines under each other
Oh that's done with \equiv

$$\equiv$$

Oh that's done with \equiv

$$\equiv$$
Cheers!

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

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

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.

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

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

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

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

I think that is correct, thank you!