QuestionAugust 10, 2025

Solve: x^2-4x+13=0 Identify the type of roots

Solve: x^2-4x+13=0 Identify the type of roots
Solve: x^2-4x+13=0 Identify the type of roots

Solution
4.7(108 votes)

Answer

Two complex conjugate roots. Explanation 1. Calculate the Discriminant The discriminant \Delta is calculated using **\Delta = b^2 - 4ac**. Here, a=1, b=-4, and c=13. So, \Delta = (-4)^2 - 4 \cdot 1 \cdot 13 = 16 - 52 = -36. 2. Determine the Type of Roots Since \Delta < 0, the equation has two complex conjugate roots.

Explanation

1. Calculate the Discriminant<br /> The discriminant $\Delta$ is calculated using **$\Delta = b^2 - 4ac$**. Here, $a=1$, $b=-4$, and $c=13$. So, $\Delta = (-4)^2 - 4 \cdot 1 \cdot 13 = 16 - 52 = -36$.<br />2. Determine the Type of Roots<br /> Since $\Delta < 0$, the equation has two complex conjugate roots.
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