If \(p(x)=x^2+6x+9\), what is the nature of its zeroes?
Answer and explanation
Correct answer: Two equal real zeroes, both \(-3\)
\(p(x)=x^2+6x+9=(x+3)^2\). Thus, setting \(p(x)=0\) gives \(x=-3\), and this zero occurs twice; hence the polynomial has two equal real zeroes. Option B is incorrect because \(3\) is not a zero of this polynomial. Exam tip: for a quadratic polynomial, \(D=b^2-4ac=0\) indicates two equal zeroes.
Frequently asked questions
What is the correct answer to this question?
Two equal real zeroes, both \(-3\)
Why is this the correct answer?
\(p(x)=x^2+6x+9=(x+3)^2\). Thus, setting \(p(x)=0\) gives \(x=-3\), and this zero occurs twice; hence the polynomial has two equal real zeroes. Option B is incorrect because \(3\) is not a zero of this polynomial. Exam tip: for a quadratic polynomial, \(D=b^2-4ac=0\) indicates two equal zeroes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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