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# Solve the quadratic equations where possible? watch

1. (Original post by vectorpi)
You have to account for the extra term when the bracket is squared by subtracting (b^2)/4a^2, so in the case of 5x^2 + 9x + 3 = 0 you get:

5[x^2 + 1.8x + 0.6] = 0
X^2 + 1.8x + 0.6 = 0
(X + 0.9)^2 + 0.6 - 0.81 = 0
(X + 0.9)^2 - 0.21 = 0
(X + 0.9)^2 = 0.21
X + 0.9 = +/- sqrt(0.21)
∴ x = -0.9 +/- sqrt(0.21)
I know - silly mistake, although I recommend keeping it in fractional form.
2. (Original post by Andy98)
I know - silly mistake, although I recommend keeping it in fractional form.
I tend to prefer fractions too as they avoid rounding errors, but as I don't have latex it would've been a nightmare to follow haha
3. (Original post by Zacken)
Oh sorry, I didn't see that!
4. (Original post by vectorpi)
I tend to prefer fractions too as they avoid rounding errors, but as I don't have latex it would've been a nightmare to follow haha
If you want to learn: TSR Latex guide
5. (Original post by vectorpi)
I tend to prefer fractions too as they avoid rounding errors, but as I don't have latex it would've been a nightmare to follow haha
Nor do I. TSR does
6. (Original post by tom989)
how would i use complete the square?
Can sometimes be tricky to complete the square when your leading coefficient isn't 1 i.e 5 or 2. Just make sure you take out this coefficient out of the quadratic AND linear term.

https://youtu.be/13zWRSJaHy0?t=1308

Hope this helps,

Tom (IDK-tuition.com: online maths, economics and ACT tuition/resources)
7. (Original post by RAlexO)
there are 4 ways to solve quadratics:
1. Complete the square
3. factorise
4. graphs (yes you can use graphs to use quadratic)

You're best choices will be the formula (you find it online) and graphs (but you'll have to use excel to ensure that you get an accurate answer) - input some numbers in the formula and plot an XY scatter graph in excel and take interception of the shape with X line ... it should work very well
5. Fixed Point Iteration
6. Newton Raphson Method
8. (Original post by the bear)
5. Fixed Point Iteration
6. Newton Raphson Method
7. Linear interpolation.
8. Interval bisection.
9. (Original post by Zacken)
7. Linear interpolation.
8. Interval bisection.
9. Simultaneous Equations if you know two points
10. (Original post by the bear)
9. Simultaneous Equations if you know two points
10. Solving the simultaneous equations using matrices if you know two points.
11. Matrices and eigenvalues/vectors method.
11. (Original post by the bear)
9. Simultaneous Equations if you know two points
What? Teach me...
12. (Original post by EricPiphany)
What? Teach me...
if y = x2 +bx +c

passes through the points ( 0, 6 ) and ( 1, 2 ) then you can find b & c
13. (Original post by the bear)
if y = x2 +bx +c

passes through the points ( 0, 6 ) and ( 1, 2 ) then you can find b & c
That gets you the quadratic equation, doesn't get you the roots of it though.
14. (Original post by Zacken)
10. Solving the simultaneous equations using matrices if you know two points.
11. Matrices and eigenvalues/vectors method.
12. Product and sum of roots method.
15. (Original post by Zacken)
12. Product and sum of roots method.
I recommend method 101: Multiply through by a five dimensional matrix, take the Fourier transform, and then it's just a simple volume integral from there.
16. (Original post by Zacken)
10. Solving the simultaneous equations using matrices if you know three points.
11. Matrices and eigenvalues/vectors method.
an interesting collection of methods is given here:

17. (Original post by EricPiphany)
I recommend method 101: Multiply through by a five dimensional matrix, take the Fourier transform, and then it's just a simple volume integral from there.
The proof is trivial! Just biject it to a combinatorial module whose elements are thrice-differentiable metric spaces.

Gold comedy: http://www.theproofistrivial.com/
18. (Original post by Zacken)
That gets you the quadratic equation, doesn't get you the roots of it though.
19. (Original post by the bear)
Had a quick scroll through the PDF you sent, some of those methods are pretty cool. I think the trigonometric one came up under guise in my STEP 2015, I exam.
20. (Original post by Zacken)
Had a quick scroll through the PDF you sent, some of those methods are pretty cool. I think the trigonometric one came up under guise in my STEP 2015, I exam.
#18 ftw

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