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

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Solving Quadratic Equations (-b Formula)

Solving quadratics for $x$ can be done using the quadratic formula :

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

Example

infoNote

Solve for $x$

2x^2-7x+3=0

Identify the coefficients :

a=2,b=-7,c=3

Substitute into the formula :

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

Simplify :

x = \frac{7 \pm \sqrt{49 - 24}}{4}

x = \frac{7 \pm \sqrt{25}}{4}

x = \frac{7 + 5}{4} = \frac{12}{4} = :success[3]

x = \frac{7 - 5}{4} = \frac{2}{4} = :success[\frac{1}{2}]

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