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C2 - Solving trig equation mistake

This question is from C2 Edexcel June 2013, Q8 part (ii) (b)

I let cos theta = x for typing faster.

4x^2 + 2x -1 = 0

I used completing the square

4(x^2+x/2)-1=0

4(x+1/4)^2-(1/16)-1=0

4(x+1/4)^2=17/16

(x+1/4)^2=17/64


(x+1/4)= root (17/64)

x=-1/4 plus or minus root (17/64)


That gives x, or cos theta, = 0.265.... or =-0.265....

This isn't correct, can anyone please tell me what I've done wrong?
Reply 1
Avatar for Zacken
Zacken
22
Original post by jamb97
This question is from C2 Edexcel June 2013, Q8 part (ii) (b)

I let cos theta = x for typing faster.

4x^2 + 2x -1 = 0

I used completing the square

4(x^2+x/2)-1=0

4(x+1/4)^2-(1/16)-1=0

4(x+1/4)^2=17/16


Bolded bits. You should review completing the square again or how to expand brackets.

4((x+0.25)2−116)−1=0  ⟺  4(x+0.25)2−416−1=04\bigg((x + 0.25)^2 - \frac{1}{16}\bigg) - 1 = 0 \iff 4(x+0.25)^2 - \frac{4}{16} - 1 = 0

This gives 4(x+0.25)2=54≠1716 4(x + 0.25)^2 = \frac{5}{4} \neq \frac{17}{16}
Reply 2
Avatar for jamb97
jamb97
OP
2
Original post by Zacken
Bolded bits. You should review completing the square again or how to expand brackets.

4((x+0.25)2−116)−1=0  ⟺  4(x+0.25)2−416−1=04\bigg((x + 0.25)^2 - \frac{1}{16}\bigg) - 1 = 0 \iff 4(x+0.25)^2 - \frac{4}{16} - 1 = 0

This gives 4(x+0.25)2=54≠1716 4(x + 0.25)^2 = \frac{5}{4} \neq \frac{17}{16}
Woops... Got it. Thanks very much :smile:
Reply 3
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Zacken
22
Original post by jamb97
Woops... Got it. Thanks very much :smile:


Using big brackets when you have nested expressions like these are very useful for avoiding these types of mistakes. :smile:
Original post by jamb97
-


Alternatively you could just use the quadratic formula to avoid silly mistakes.
Reply 5
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Zacken
22
Original post by edothero
Alternatively you could just use the quadratic formula to avoid silly mistakes.


Or make more silly mistakes using the quadratic formula. :tongue:
Original post by Zacken
Or make more silly mistakes using the quadratic formula. :tongue:


I can relate to that statement :laugh:
Reply 7
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Zacken
22
Original post by edothero
I can relate to that statement :laugh:


Me 2 years ago in GCSE:

2 kul for u bby imma use quadratic formula

#negative discriminant

imaginary numbers betch
Original post by Zacken
Me 2 years ago in GCSE:

2 kul for u bby imma use quadratic formula

#negative discriminant

imaginary numbers betch


lmaooo I remember once when I was ill I had a c3 mock, started using complex numbers thinking I was doing fp2. Facepalms were real
Reply 9
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Zacken
22
Original post by edothero
lmaooo I remember once when I was ill I had a c3 mock, started using complex numbers thinking I was doing fp2. Facepalms were real


:rofl:

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