Solve \(x^2-8 x-9 \leq 0\). (2 marks) --- 4 WORK AREA LINES (style=lined) ---
\(\therefore -1 \leqslant x \leqslant 9\)
Show Worked Solution
\(x^2-8 x-9 \leqslant 0\)
\((x-9)(x+1) \leqslant 0\)
Functions, EXT1 F1 SM-Bank 17
Solve the inequality `x^2<=|\ 2x-1\ |` for `x`.
Express your answer in interval notation. (3 marks)
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Functions, EXT1 F1 2020 HSC 1 MC
Which diagram best represents the solution set of `x^2 - 2x - 3 >= 0`?
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B. |  |
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Functions, EXT1 F1 SM-Bank 1
Find the values of `x` that satisfy the equation
`x^2 + 8x + 3 <= 0`. (3 marks)
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Show Worked Solution
| `x` | `= (-8 ± sqrt(8^2-4 · 1 · 3))/2` |
| `= (-8 ± sqrt(52))/2` | |
| `= -4 ± sqrt13` |
`{x:\ -4-sqrt13 <=x <= -4 + sqrt13}`
Functions, EXT1* F1 2010 HSC 2b
Solve the inequality `x^2 − x − 12 < 0`. (2 marks)
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Show Worked Solution
MARKER’S COMMENT: Drawing the parabola proved the most efficient way of answering this question for students.
`x^2\ – x\ – 12<0`
| `text(Solve)\ \ \ ` | `x^2\ – x\ – 12` | `=0` |
| `(x\ – 4)(x + 3)` | `=0` | |
| `=>x = 4\ text(or)\ -3` | ||
`x^2 – x – 12 < 0`
`text(when)\ \ -3 < x < 4`