What is the value of the discriminant \(D=b^2-4ac\) for the equation \(x^2-4x+1=0\)?
Answer and explanation
Correct answer: 12
For the given equation, \(a=1\), \(b=-4\), and \(c=1\). Hence, \(D=b^2-4ac=(-4)^2-4(1)(1)=16-4=12\). Therefore, the correct answer is 12. Since \(D>0\), the roots are real and distinct; because 12 is not a perfect square, they are also irrational. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
For the given equation, \(a=1\), \(b=-4\), and \(c=1\). Hence, \(D=b^2-4ac=(-4)^2-4(1)(1)=16-4=12\). Therefore, the correct answer is 12. Since \(D>0\), the roots are real and distinct; because 12 is not a perfect square, they are also irrational. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
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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