Mathematics Chapter 2 Questions

Mathematics are like games x)

 

If you manage to handle it,

Or even , win it...

You might even get an A++ for it! =)

You can play it in any ways..

Some even play it using this x)

And by multiplying in fun ways!

For example :

Now, Im goin to show you The Quadratic Equations and how you solve,

Or like what I might call it,

How to "play" it x)

1)

2x(x – 3) = (2 – x)(x + 1)
2x2 – 6x = 2x + 2 – x2 – x
3x2 – 7x – 2 = 0
x =
– (–7) ± (–7)2 – 4(3)(–2)
2(3)
x =
7 ± 49 + 24
6
x = 7 ± 8.5440
6
x = 2.591 or –0.2573

2) The roots are 2
3
and – 5
2
.
Sum of roots = 2
3
+ – 5
2 = – 11
6
Product of roots = 2
3
× – 5
2 = – 5
3
The quadratic equation is
x2 + 11
6
x – 5
3
= 0
6x2 + 11x – 10 = 0
x2 – (sum of roots)x + (product of roots) = 0

 

3) y = 5x – 2 … 1
y = 3x2 + 3x + k … 2
Substituting 2 into 1 :
3x2 + 3x + k = 5x – 2
3x2 – 2x + k + 2 = 0
a = 3, b = –2, c = k + 2
In the case where a curve does not meet a straight
line, b2 – 4ac < 0 is applied.
b2 – 4ac < 0
(–2)2 – 4(3)(k + 2) < 0
4 – 12k – 24 < 0
–12k – 20 < 0
–12k < 20
k > 20
–12
k > –12
3

4) 7 – 2(1 + x)2 = x(x + 5)
7 – 2(1 + 2x + x2) = x2 + 5x
7 – 2 – 4x – 2x2 = x2 + 5x
3x2 + 9x – 5 = 0
x =
–b ± b2 – 4ac
2a
x =
–9 ± 92 – 4(3)(–5)
2(3)
x =
–9 ± 141
6
x = 0.4791 or –3.479

5) 9x2 + qx + 1 = 4x
9x2 + qx – 4x + 1 = 0
9x2 + (q – 4)x + 1 = 0
a = 9, b = q – 4, c = 1 

If the equation has equal roots, then
b2 – 4ac = 0
(q – 4)2 – 4(9)(1) = 0
q2 – 8q + 16 – 36 = 0
q2 – 8q – 20 = 0
(q + 2)(q – 10) = 0

q = –2 or 10