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Functions, 2ADV EQ-Bank 08

Solve for \(x\), giving your answers in the simplest form  \(a+b\sqrt{c}\)  where \(a, b\) and \(c\) are real:

\(5 x^2-20 x+4=0\)   (2 marks)

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\(x=2 \pm \dfrac{4}{5} \sqrt{5}\)

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\(5 x^2-20 x+4=0\)

\(x\) \(=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)
  \(=\dfrac{20 \pm \sqrt{20^2-4 \times 5 \times 4}}{2 \times 5}\)
  \(=\dfrac{20 \pm \sqrt{320}}{10}\)
  \(=2 \pm \dfrac{8 \sqrt{5}}{10}\)
  \(=2 \pm \dfrac{4}{5} \sqrt{5}\)

Functions, 2ADV EQ-Bank 7 MC

What are the solutions to  \(3x^2+2x-4=0\)?

  1. \(x=\dfrac{-1 \pm \sqrt{13}}{3}\)
  2. \(x=\dfrac{1 \pm \sqrt{13}}{3}\)
  3. \(x=\dfrac{-1 \pm \sqrt{5}}{2}\)
  4. \(x=\dfrac{1 \pm \sqrt{5}}{2}\)
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\(A\)

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\(3 x^2+2 x-4=0\)

\(x\) \(=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2a}\)
  \(=\dfrac{-2 \pm \sqrt{2^2-4 \times 3 \times-4}}{2 \times 3}\)
  \(=\dfrac{-2 \pm \sqrt{52}}{6}\)
  \(=\dfrac{-1 \pm \sqrt{13}}{3}\)

 

\(\Rightarrow A\)

Functions, 2ADV F1 2013 HSC 1 MC

What are the solutions of   `2x^2-5x-1 = 0`? 

  1. `x = (-5 +-sqrt17)/4` 
  2. `x = (5 +-sqrt17)/4`
  3. `x = (-5 +-sqrt33)/4`
  4. `x = (5 +-sqrt33)/4`
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`D`

Show Worked Solution

`2x^2-5x-1 = 0`

`text(Using)\ x = (-b +- sqrt( b^2-4ac) )/(2a)`

`x` `= (5 +- sqrt{\ \ (-5)^2-4 xx 2 xx(-1) })/ (2 xx 2)`
  `= (5 +- sqrt(25 + 8) )/4`
  `= (5 +- sqrt(33) )/4`

 
`=>  D`