If the zeros of a quadratic polynomial are \(5+\sqrt{3}\) and \(5-\sqrt{3}\), what is their product?
Answer and explanation
Correct answer: 22
Core idea: conjugate pairs use the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\). Here \(a=5\) and \(b=\sqrt{3}\), so the product is \((5+\sqrt{3})(5-\sqrt{3})=5^2-(\sqrt{3})^2=25-3=22\). Option D (\(25+\sqrt{3}\)) is incorrect because it is a sum not the result of difference of squares; B and C arise from simple arithmetic mistakes. Exam tip: on seeing conjugate zeros, apply \((a+b)(a-b)\) immediately to avoid extra steps and errors.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Core idea: conjugate pairs use the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\). Here \(a=5\) and \(b=\sqrt{3}\), so the product is \((5+\sqrt{3})(5-\sqrt{3})=5^2-(\sqrt{3})^2=25-3=22\). Option D (\(25+\sqrt{3}\)) is incorrect because it is a sum not the result of difference of squares; B and C arise from simple arithmetic mistakes. Exam tip: on seeing conjugate zeros, apply \((a+b)(a-b)\) immediately to avoid extra steps and errors.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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