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To factorise a trinomial \(x^2+bx+c\), whose leading coefficient is 1, in the form \((x+p)(x+q)\), what relation must \(p\) and \(q\) satisfy?
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Answer and explanation
Correct answer: \(p+q=b\) and \(pq=c\)
\((x+p)(x+q)=x^2+(p+q)x+pq\). Hence, the sum of the two numbers must give the coefficient of \(x\), and their product must give the constant term. Exam tip: check product first, then sum.
Frequently asked questions
What is the correct answer to this question?
\(p+q=b\) and \(pq=c\)
Why is this the correct answer?
\((x+p)(x+q)=x^2+(p+q)x+pq\). Hence, the sum of the two numbers must give the coefficient of \(x\), and their product must give the constant term. Exam tip: check product first, then sum.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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