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Home / Algebra / Solving Equations and Inequalities / Quadratic Equations : A Summary
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Section 2.7 : Quadratic Equations : A Summary

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

\[49{x^2} - 126x + 102 = 0\]

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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.

\[a = 49\hspace{0.25in}\hspace{0.25in}b = - 126\hspace{0.25in}\hspace{0.25in}c = 102\] Show Step 2

Plugging these into the formula for the discriminant gives,

\[{b^2} - 4ac = {\left( { - 126} \right)^2} - 4\left( {49} \right)\left( {102} \right) = - 4116\] Show Step 3

The discriminant is negative and so we know that this equation will have two complex roots.