Solving Quadratic Equations (-b Formula) (Leaving Cert Mathematics): Revision Notes

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Solving Quadratic Equations (-b Formula)

Solving quadratics for xx can be done using the quadratic formula :

x=−b±b2−4ac2ax=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

Example

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Solve for xx

2x2−7x+3=02x^2-7x+3=0

Identify the coefficients :

a=2,b=−7,c=3a=2,b=-7,c=3

Substitute into the formula :

x=−(−7)±(−7)2−4(2)(3)2(2)x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(3)}}{2(2)}

Simplify :

x=7±49−244x = \frac{7 \pm \sqrt{49 - 24}}{4} x=7±254x = \frac{7 \pm \sqrt{25}}{4} x=7+54=124=:success[3]x = \frac{7 + 5}{4} = \frac{12}{4} = :success[3]x=7−54=24=:success[12]x = \frac{7 - 5}{4} = \frac{2}{4} = :success[\frac{1}{2}]

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