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Problem #59

Find the value of

\displaystyle |\alpha -\beta |

for the two roots

\displaystyle \alpha ,\beta

of the quadratic equation

\displaystyle 2x^{2}+8x+1=0

Grade Result

Incorrect

By the relationship between the roots and coefficients of a quadratic equation:

\displaystyle \alpha +\beta =-4

\displaystyle \alpha \beta =\frac{1}{2}

\displaystyle \therefore (\alpha -\beta )^{2}=\left( \alpha +\beta \right)^{2}+4\alpha \beta

😢 Let's try that again and double-check our work. It should be

\displaystyle (\alpha -\beta )^{2}=\left( \alpha +\beta \right)^{2}-4\alpha \beta

\displaystyle =\left( -4 \right)^{2}+4 \times \frac{1}{2}

\displaystyle =16+2

\displaystyle =18

\displaystyle \therefore |\alpha -\beta |=3\sqrt{2}

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