Algebra - Quadratic Equations : A Summary

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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.