If the zeroes of a monic quadratic polynomial are \(a+\sqrt{b}\) and \(a-\sqrt{b}\), what is its discriminant?

\(4b\)

With roots \(a+\sqrt{b}\) and \(a-\sqrt{b}\), the sum of roots is \(2a\) and the product is \(a^{2}-b\). The monic quadratic is \(x^{2}-2ax+(a^{2}-b)\). Its discriminant is \(\Delta=(2a)^{2}-4\cdot1\cdot(a^{2}-b)=4a^{2}-4a^{2}+4b=4b\), so \(4b\) is correct. Closest distractor D equals \(4(a^{2}-b)=4a^{2}-4b\), which is generally different from \(4b\); option C ignores the subtraction in the product and B would only hold if \(b=0\). Exam tip: use sum and product of roots to form the quadratic quickly, then compute \(\Delta\) from its coefficients.

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