If \((x+a)^2 = x^2 + 28x + 196\), what is the value of \(a\)?
Answer and explanation
Correct answer: 14
Using the identity \((x+a)^2 = x^2 + 2ax + a^2\), compare coefficients with \(x^2 + 28x + 196\). From the coefficient of \(x\) we get \(2a = 28\), so \(a = 14\). Also \(a^2 = 196\) holds for \(a=14\). The option \(-14\) is incorrect because it would give \(2a = -28\), which contradicts the given linear coefficient. Exam tip: equate coefficients of like powers of \(x\) to find unknown parameters quickly.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Using the identity \((x+a)^2 = x^2 + 2ax + a^2\), compare coefficients with \(x^2 + 28x + 196\). From the coefficient of \(x\) we get \(2a = 28\), so \(a = 14\). Also \(a^2 = 196\) holds for \(a=14\). The option \(-14\) is incorrect because it would give \(2a = -28\), which contradicts the given linear coefficient. Exam tip: equate coefficients of like powers of \(x\) to find unknown parameters quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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