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Surds

Hey guys,

I've never really liked surds, and I need help! :smile:

Does someone mind just going through this quick question for me with steps also:

1) x^2+12x+20=0 solve the following equation giving answer in surd form.

Does this mean working it out via completing the square?
Thank you!

Reply 1

shawn_o1

yes:
(x + 6)^2 - 36 + 20 = 0
(x + 6)^2 = 16

(The final answer is not really a surd :s-smilie:

)

Reply 2

Zen-Ali

Original post by rm_27

...

Not necessarily, I think; it just means they want your answer in an 'exact' form—hence a surd. Therefore, it doesn't matter which method you use to solve it.

For example, consider

x^2 = 3 \implies x = \pm \sqrt{3}

.

You could, if asked, leave it as a truncated decimal (i.e. rounded to a certain degree), for example to 1 decimal place it'd be

\pm 1.7

, however in this case you leave it as a surd.

The answer(s), however, are integers for your question, but if otherwise they specify a surd then leave it in the exact form, as above.

Reply 3

samuelsc

I used to get these questions all the time in GCSE, what I would do is complete the square, then throw over the power of two to get X by itself

(x+6)^2-36+20=0
(x+6)^2-16=0
(x+6)^2=16
(x+6)=±√16
x = -6±√16

Hope that helped at all :smile:

Reply 4

TenOfThem

Original post by rm_27

Hey guys,

I've never really liked surds, and I need help! :smile:

No surds in the answer for that particular example

(x+2)(x+10)

x= -2 or x= -10

However, surds will normally require completing the square/using the formula