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Rationalize denominator & factorising quadratic equations.

  1. Nov 1, 2015 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations
    Not Sure.

    3. The attempt at a solution

    For the first question I know you have to multiply the conjugate of the denominator so it would be (2 - √5)/(1−2√5) x (1−2√5)/(1−2√5) but I'm not sure how to actually do that.

    For the second question. I have that -3 x 2 = -6 and -3 + 2 = -1 which fits the sum. I think this is correct.

    for this second part of the second question, I'm not sure how to solve this as I don't see any factors of -6 which when added together = 11.
     
  2. jcsd
  3. Nov 1, 2015 #2

    andrewkirk

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    The first thing you need to do is to be very careful to get your signs right, which is not happening in the bit I quoted. Where has the 1+2√5 disappeared to?
    Next, when multiplying the first fraction by ##\frac{1-2\sqrt{5}}{1-2\sqrt{5}}##, just make the result a new fraction in which the numerator is the product of the numerators and the denominator is the product of the denominators. You know: $$\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$$.
     
  4. Nov 1, 2015 #3

    andrewkirk

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    You won't be able to use that simple rule, because the ##x^2## has a coefficient other than 1.

    Instead set ##(2x+a)(x+b)## equal to the quadratic. Expand the brackets and then work out what ##a## and ##b## have to be to make the equation true for every possible value of ##x##.
     
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