QuestionAugust 27, 2025

Find the nature of the quadratic equation x^2-7x+12=0 Complex Real and equal Real and distinct Cannot be determined

Find the nature of the quadratic equation x^2-7x+12=0 Complex Real and equal Real and distinct Cannot be determined
Find the nature of the quadratic equation x^2-7x+12=0 Complex Real and equal Real and distinct Cannot be determined

Solution
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Answer

Real and distinct Explanation 1. Calculate the discriminant The discriminant \Delta is calculated using **\Delta = b^2 - 4ac**. Here, a=1, b=-7, and c=12. So, \Delta = (-7)^2 - 4 \cdot 1 \cdot 12 = 49 - 48 = 1. 2. Determine the nature of roots If \Delta > 0, the roots are real and distinct; if \Delta = 0, they are real and equal; if \Delta < 0, they are complex.

Explanation

1. Calculate the discriminant<br /> The discriminant $\Delta$ is calculated using **$\Delta = b^2 - 4ac$**. Here, $a=1$, $b=-7$, and $c=12$. So, $\Delta = (-7)^2 - 4 \cdot 1 \cdot 12 = 49 - 48 = 1$.<br />2. Determine the nature of roots<br /> If $\Delta > 0$, the roots are real and distinct; if $\Delta = 0$, they are real and equal; if $\Delta < 0$, they are complex.
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