smc-4386-40-Quadratic formula

Quadratics and Cubics, SMB-037

Using the quadratic formula, find `p` given

`p^2+2p-4 = 0.` (3 marks)

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`-1 +- sqrt(5)`

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`p^2+2p-4 = 0`

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

`p`	`= (-2 +- sqrt{(2)^2-4 xx 1 xx(-4) })/ (2 xx 1)`
	`= (-2 +- sqrt(20) )/2`
	`=(-2 +- 2sqrt(5) )/2`
	`= -1 +- sqrt(5)`

Quadratics and Cubics, SMB-036

Using the quadratic formula, find `a` given

`5a^2+7a-1 = 0.` (3 marks)

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`(-7 +- sqrt(69) )/10`

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`5a^2+7a-1 = 0`

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

`a`	`= (-7 +- sqrt{(7)^2-4 xx 5 xx(-1) })/ (2 xx 5)`
	`= (-7 +- sqrt(49+20) )/10`
	`= (-7 +- sqrt(69) )/10`

Quadratics and Cubics, SMB-035

Using the quadratic formula, solve

`3x^2-4x-2 = 0`. (3 marks)

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

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`(2 +- sqrt(10) )/3`

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`3x^2-4x-2 = 0`

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

`x`	`= (4 +- sqrt{(-4)^2-4 xx 3 xx(-2) })/ (2 xx 3)`
	`= (4 +- sqrt(16+24) )/6`
	`= (4 +- sqrt(40) )/6`
	`= (4 +- 2sqrt(10) )/6`
	`= (2 +- sqrt(10) )/3`

Functions, 2ADV F1 2013 HSC 1 MC

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

`x = (-5 +-sqrt17)/4`
`x = (5 +-sqrt17)/4`
`x = (-5 +-sqrt33)/4`
`x = (5 +-sqrt33)/4`

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`D`

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`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`