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Math Help - 5 Quadratic Equations

  1. #1
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    Red face 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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by IGCSE student View Post
    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
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  3. #3
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    what is the best method i could use to solve the equation
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by IGCSE student View Post
    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
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  5. #5
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    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.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by IGCSE student View Post
    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.)

    Consider the following quadratic:
    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
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  7. #7
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    Thanks for explaining the AC method to thoes whom dnt know, personally i understand the method completely.
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