smc-4386-30-Quadratics (Monic)

Quadratics and Cubics, SMB-030

Solve the equation `p^2-12p=64` for `p`. (2 marks)

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`p=16 \ text{or}\ -4`

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`p^2-12p`	`=64`
`p^2-12p-64`	`=0`
`(p-16)(p+4)`	`=0`

`:. p=16 \ text{or}\ -4`

Quadratics and Cubics, SMB-029

Solve the equation `14x=32-x^2` for `x`. (2 marks)

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`x=2 \ text{or}\ -16`

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`14x`	`=32-x^2`
`x^2+14x-32`	`=0`
`(x-2)(x+16)`	`=0`

`:. x=2 \ text{or}\ -16`

Quadratics and Cubics, SMB-028

Solve the equation `c^2-24=5c` for `c`. (2 marks)

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`c=8 \ text{or}\ -3`

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`c^2-24`	`=5c`
`c^2-5c-24`	`=0`
`(c-8)(c+3)`	`=0`

`:. c=8 \ text{or}\ -3`

Quadratics and Cubics, SMB-027

Solve the equation `y^2-2y-3=0` for `y`. (2 marks)

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`y=3 \ text{or}\ -1`

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`y^2-2y-3`	`=0`
`(y-3)(y+1)`	`=0`

`:. y=3 \ text{or}\ -1`

Quadratics and Cubics, SMB-025

Solve the equation `t^2-8t+12=0` for `t`. (2 marks)

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`:. t=6 \ text{or}\ 2`

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`t^2-8t+12`	`=0`
`(t-6)(t-2)`	`=0`

`:. t=6 \ text{or}\ 2`

Algebra, STD2 A1 2005 HSC 24c

Make `L` the subject of the equation `T = 2piL^2`. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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`± sqrt(T/(2pi))`

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`T`	`= 2piL^2`
`L^2`	`= T/(2pi)`
`:.L`	`= ±sqrt(T/(2pi))`

Functions, 2ADV F1 2010 HSC 1a

Solve `x^2 = 4x`. (2 marks)

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`x = 0\ text(or)\ 4`

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`x^2`	`= 4x`
`x^2-4x`	`= 0`
`x(x-4)`	`= 0`

`:.\ x = 0\ text(or)\ 4`