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### Section 2.7 : Quadratic Equations : A Summary

1. Use the discriminant to determine the type of roots for the following equation. Do not find any roots.

$169{x^2} - 182x + 49 = 0$

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Start Solution

There really isn’t too much to this problem. First, we need to identify the values for computing the discriminant.

$a = 169\hspace{0.25in}\hspace{0.25in}b = - 182\hspace{0.25in}\hspace{0.25in}c = 49$ Show Step 2

Plugging these into the formula for the discriminant gives,

${b^2} - 4ac = {\left( { - 182} \right)^2} - 4\left( {169} \right)\left( {49} \right) = 0$ Show Step 3

The discriminant is zero and so we know that this equation will have a double root.