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$b_{2}−4ac$

SubstituteValuesSubstitute values

$2_{2}−4(8)(-1)$

Simplify

CalcPowCalculate power

$4−4(8)(-1)$

MultiplyMultiply

$4−32(-1)$

MultNegNegOnePar$-a(-b)=a⋅b$

$4+32$

AddTermsAdd terms

$36$

b

We want to use the discriminant of the given quadratic equation to determine the number and type of the roots. If we don't want to know the exact values of the roots, we only need to work with the discriminant. From Part A, we know that the discriminant of the given equation is $36.$
$Equation:Discriminant: 8x_{2}=-2x+136 $
Since the discriminant is *greater than zero* and a perfect square, the quadratic equation has two rational roots.

c

$x=16-2±6 $ | |
---|---|

$x_{1}=16-2+6 $ | $x_{2}=16-2−6 $ |

$x_{1}=164 $ | $x_{2}=16-8 $ |

$x_{1}=41 $ | $x_{2}=-21 $ |

Using the Quadratic Formula, we found that the solutions of the given equation are $x_{1}=41 $ and $x_{2}=-21 .$