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A student incorrectly writes the discriminant as \(D=b^2+4ac\). What is the correct discriminant \(D\) for the quadratic equation \(x^2+2x+3=0\)?
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Answer and explanation
Correct answer: -8
For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\). Here, \(a=1\), \(b=2\), and \(c=3\), so \(D=2^2-4(1)(3)=4-12=-8\). The value 16 results from using the incorrect formula \(b^2+4ac\). Exam tip: remember the discriminant formula as \(b^2-4ac\).
Frequently asked questions
What is the correct answer to this question?
-8
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\). Here, \(a=1\), \(b=2\), and \(c=3\), so \(D=2^2-4(1)(3)=4-12=-8\). The value 16 results from using the incorrect formula \(b^2+4ac\). Exam tip: remember the discriminant formula as \(b^2-4ac\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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