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If \(a,b,c\) are integers and \(a\ne0\), which condition identifies that the quadratic equation \(ax^2+bx+c=0\) has two distinct irrational real roots?
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Answer and explanation
Correct answer: \(\Delta>0\) and \(\Delta\) is not a perfect square
Here \(\Delta=b^2-4ac\). When \(\Delta>0\), the roots are real and distinct; if it is not a perfect square, \(\sqrt{\Delta}\) is irrational. In exams, check the sign of \(\Delta\) first and then whether it is a perfect square.
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What is the correct answer to this question?
\(\Delta>0\) and \(\Delta\) is not a perfect square
Why is this the correct answer?
Here \(\Delta=b^2-4ac\). When \(\Delta>0\), the roots are real and distinct; if it is not a perfect square, \(\sqrt{\Delta}\) is irrational. In exams, check the sign of \(\Delta\) first and then whether it is a perfect square.
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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