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Worked solution

Find exact quadratic roots

Find the exact roots of the equation 3x2−6x+2=03x^2-6x+2=0.

CJC · Discussion · Question 3

Answer

x=1±3/3x=1\pm\sqrt3/3.

Apply the quadratic formula

x=6±62−4(3)(2)6=1±126=1±33x=\dfrac{6\pm\sqrt{6^2-4(3)(2)}}6=1\pm\dfrac{\sqrt{12}}6=1\pm\dfrac{\sqrt3}3.

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Common mistakes

An exact answer keeps the surd rather than a decimal approximation.

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