For a quadratic equation \(ax^2+bx+c=0\) with integer coefficients, where \(a\ne0\), which condition on the discriminant \(D=b^2-4ac\) identifies two distinct irrational roots?
Answer and explanation
Correct answer: When \(D>0\) and \(D\) is not a perfect square
When \(D>0\), the roots are real and distinct. With integer coefficients, if \(D\) is not a perfect square, \(\sqrt D\) is irrational, so both roots are irrational. Exam tip: check the sign of \(D\) first, then test whether it is a perfect square.
Frequently asked questions
What is the correct answer to this question?
When \(D>0\) and \(D\) is not a perfect square
Why is this the correct answer?
When \(D>0\), the roots are real and distinct. With integer coefficients, if \(D\) is not a perfect square, \(\sqrt D\) is irrational, so both roots are irrational. Exam tip: check the sign of \(D\) first, then test 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
