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Which of the following quadratic equations has real and distinct roots that are irrational?
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Answer and explanation
Correct answer: \(x^2-2x-1=0\)
For \(x^2-2x-1=0\), the discriminant is \(D=b^2-4ac=(-2)^2-4(1)(-1)=8\). Since \(D>0\), the roots are real and distinct; since 8 is not a perfect square, they are irrational. Exam tip: use the discriminant to classify roots.
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What is the correct answer to this question?
\(x^2-2x-1=0\)
Why is this the correct answer?
For \(x^2-2x-1=0\), the discriminant is \(D=b^2-4ac=(-2)^2-4(1)(-1)=8\). Since \(D>0\), the roots are real and distinct; since 8 is not a perfect square, they are irrational. Exam tip: use the discriminant to classify roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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