Using the quadratic formula, what is the value of the discriminant \(D\) for the equation \(2x^2-4x-3=0\)?
Answer and explanation
Correct answer: 40
In the standard form \(ax^2+bx+c=0\), we have \(a=2\), \(b=-4\), and \(c=-3\). Thus, \(D=b^2-4ac=(-4)^2-4(2)(-3)=16+24=40\). Since \(c\) is negative, the term \(-4ac\) becomes positive. Exam tip: identify the signs of \(a\), \(b\), and \(c\) before substituting; taking only \(b^2=16\) is incorrect.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
In the standard form \(ax^2+bx+c=0\), we have \(a=2\), \(b=-4\), and \(c=-3\). Thus, \(D=b^2-4ac=(-4)^2-4(2)(-3)=16+24=40\). Since \(c\) is negative, the term \(-4ac\) becomes positive. Exam tip: identify the signs of \(a\), \(b\), and \(c\) before substituting; taking only \(b^2=16\) is incorrect.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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