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What is the value of the discriminant \(D\) used in the quadratic formula for the equation \(5x^2-10x-3=0\)?
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Answer and explanation
Correct answer: 160
Comparing the equation with \(ax^2+bx+c=0\), we get \(a=5\), \(b=-10\), and \(c=-3\). Thus, \(D=b^2-4ac=(-10)^2-4(5)(-3)=100+60=160\). Since \(c\) is negative, the term \(-4ac\) becomes positive. Exam tip: write the sign of \(b\) explicitly before squaring it.
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What is the correct answer to this question?
160
Why is this the correct answer?
Comparing the equation with \(ax^2+bx+c=0\), we get \(a=5\), \(b=-10\), and \(c=-3\). Thus, \(D=b^2-4ac=(-10)^2-4(5)(-3)=100+60=160\). Since \(c\) is negative, the term \(-4ac\) becomes positive. Exam tip: write the sign of \(b\) explicitly before squaring it.
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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