If a quadratic polynomial has zeroes with sum \(5\sqrt{2}\) and product \(12\), which polynomial represents it?

x^2-5\sqrt{2}x+12

For a monic quadratic the relation is \(x^2-Sx+P\), where \(S\) is the sum of the roots and \(P\) their product. With \(S=5\sqrt{2}\) and \(P=12\) the polynomial is \(x^2-5\sqrt{2}x+12\). Option B has the wrong sign on the linear term; for \(x^2+5\sqrt{2}x+12\) the sum of roots would be \(-5\sqrt{2}\), not \(+5\sqrt{2}\). Options C and D do not match the given sum and product either. Exam tip: Use \(x^2-(\text{sum})x+(\text{product})\) for monic quadratics and double-check signs of coefficients.

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