Math Help - 5 Quadratic Equations

Hi there,
There are some questions in my homework which i totally dont understand.
This homework is due in wednesday 8:30am.

here they are

Solve by forming a quadratic equation

1) The length of a rectangle exceeds the width by 2cm. If the diagonal is 10cm long, find the width of the rectangle. ( use Pythagoras' Theorem)

2) The perimeter of a rectangle is 68cm. I f the diagonal is 26cm, find the dimensions of the rectangle.

3) A man walks a certain distance due North and then the same distance plus a futher 7km due east. If the final distance for the starting point is 17km, find the distance he walks from North to East.

4)A boy buys x eggs at (x-8) cents on each and (x-2) rashers of bacon at (x-3) cent each. If the total bill was \$1.75, how many eggs does he buy?

5) A number exceeds four times its reciprocal by 3. Find the number

Thanks

2. Originally Posted by IGCSE student
Hi there,
There are some questions in my homework which i totally dont understand.
This homework is due in wednesday 8:30am.

here they are

Solve by forming a quadratic equation

1) The length of a rectangle exceeds the width by 2cm. If the diagonal is 10cm long, find the width of the rectangle. ( use Pythagoras' Theorem)
Always start by assigning the variables in the problem names.

Let the length be x, and the width be y. Then we are told that x=y+2, and
the diagonal is 10cm, so by Pythagoras' theorem:

100 = x^2+y^2 = (y+2)^2+y^2,

so:

2y^2 + 4y - 96 = 0

which is for you to now solve.

RonL

3. what is the best method i could use to solve the equation

4. Originally Posted by IGCSE student
what is the best method i could use to solve the equation
Factoring, if it works, is probably the best way.

If it doesn't factor, I recommend completing the square as a good exercise, but if you need the answer fast, you can use the quadratic equation.

-Dan

5. ac

have any of u heard of the ac method?
its a new method that was introduced last year, and its being used in the IGCSE coarse.

6. Originally Posted by IGCSE student
have any of u heard of the ac method?
its a new method that was introduced last year, and its being used in the IGCSE coarse.
It is a method used to factor quadratics. (And it isn't new. It's pretty old, actually.)

$2x^2 - x - 6$

Multiply the coefficient of the $x^2$ term by the constant term. In this case, $2 \cdot -6 = -12$.

Now write all the pairs of factors of this number:
1, -12
2, -6
3, -4
4, -3
6, -2
12, -1

Now you look for a pair of those factors that add up to the coefficient of the $x$ term, in this case -1:
3 + -4 = -1
(If you cannot find such a pair, the quadratic does not factor over the rationals and you have to use another method.)

So rewrite the linear term of the quadratic using this pair of numbers:
$2x^2 - x - 6 = 2x^2 + (3x - 4x) - 6$

Now regroup it like this:
$(2x^2 + 3x) + (-4x - 6)$

and finally, factor it by grouping:
$(2x^2 + 3x) + (-4x - 6) = x(2x + 3) - 2(2x + 3)$

$= (x - 2)(2x + 3)$

Now you apply this method to solve $2y^2 + 4y - 96 = 0$. (Hint: Factor out the 2 common to all terms first.)

-Dan

7. Thanks for explaining the AC method to thoes whom dnt know, personally i understand the method completely.