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Section 2.7 : Quadratic Equations : A Summary

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

\[{x^2} + 28x + 61 = 0\]

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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.

\[a = 1\hspace{0.25in}\hspace{0.25in}b = 28\hspace{0.25in}\hspace{0.25in}c = 61\] Show Step 2

Plugging these into the formula for the discriminant gives,

\[{b^2} - 4ac = {\left( {28} \right)^2} - 4\left( 1 \right)\left( {61} \right) = 540\] Show Step 3

The discriminant is positive and so we know that this equation will have two real roots.