If \(\alpha\) and \(\beta\) are zeroes of \(x^2-7x+5\), what type of numbers are \(\alpha\) and \(\beta\)?

Both irrational real numbers

For a quadratic, the discriminant is \(D=b^2-4ac\). Here \(a=1, b=-7, c=5\), so \(D=(-7)^2-4\cdot1\cdot5=49-20=29\). Since \(D>0\) and \(29\) is not a perfect square, the equation has two distinct real irrational roots: \((7\pm\sqrt{29})/2\). Option B is incorrect because a non-perfect-square discriminant does not yield rational roots; option D is incorrect because both roots contain \(\sqrt{29}\) and are therefore both irrational. Exam tip: compute the discriminant first — if positive and not a perfect square, expect two irrational real roots.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.