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Question
Determine the nature of root of the quadratic equation.
\[3 x^2 - 5x + 7 = 0\]
Solution
\[3 x^2 - 5x + 7 = 0\]
In order to find the nature of the roots we need to find the discriminant.
\[D = b^2 - 4ac\]
\[a = 3, b = - 5, c = 7\]
\[D = \left( - 5 \right)^2 - 4 \times 3 \times 7 = 25 - 84 = - 59\]
Since, the D < 0 so, there is no real root.
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