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Under which condition will the quadratic expression \(x^2+bx+c\) be a perfect-square trinomial?
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Answer and explanation
Correct answer: \(b^2=4c\)
A perfect-square trinomial has the form \((x+a)^2=x^2+2ax+a^2\). Thus \(b=2a\) and \(c=a^2\), giving \(b^2=4c\). Option C misses the factor 4. Exam tip: halve the middle coefficient and square it.
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What is the correct answer to this question?
\(b^2=4c\)
Why is this the correct answer?
A perfect-square trinomial has the form \((x+a)^2=x^2+2ax+a^2\). Thus \(b=2a\) and \(c=a^2\), giving \(b^2=4c\). Option C misses the factor 4. Exam tip: halve the middle coefficient and square it.
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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