Algebra - Quadratic Equations : A Summary

Show All Notes Hide All Notes

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

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

Show All Steps Hide All Steps

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.