In which of the following forms can the equation \(x^2+14x+49=0\) be written?
Answer and explanation
Correct answer: \((x+7)^2=0\)
In \(x^2+14x+49\), we have \(49=7^2\) and the middle term is \(14x=2\times7\times x\). Therefore, it is the perfect square \((x+7)^2\), so the equation can be written as \((x+7)^2=0\). Option B would produce the middle term \(-14x\). In exams, match the expression with \(a^2+2ab+b^2=(a+b)^2\).
Frequently asked questions
What is the correct answer to this question?
\((x+7)^2=0\)
Why is this the correct answer?
In \(x^2+14x+49\), we have \(49=7^2\) and the middle term is \(14x=2\times7\times x\). Therefore, it is the perfect square \((x+7)^2\), so the equation can be written as \((x+7)^2=0\). Option B would produce the middle term \(-14x\). In exams, match the expression with \(a^2+2ab+b^2=(a+b)^2\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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