If the two roots of the equation \(x^2-2(m+2)x+(m+2)^2=0\) are equal, which statement about \(m\) is correct?
Answer and explanation
Correct answer: Every real \(m\)
The equation can be rewritten as \((x-(m+2))^2=0\). Hence its repeated root is \(x=m+2\), and the roots are equal for every real value of \(m\). Therefore, option A is correct. Option C gives only the special case \(m=-2\), not the complete set of valid values. Exam tip: in such questions, first look for a perfect square or verify that the discriminant \(D=b^2-4ac\) is zero.
Frequently asked questions
What is the correct answer to this question?
Every real \(m\)
Why is this the correct answer?
The equation can be rewritten as \((x-(m+2))^2=0\). Hence its repeated root is \(x=m+2\), and the roots are equal for every real value of \(m\). Therefore, option A is correct. Option C gives only the special case \(m=-2\), not the complete set of valid values. Exam tip: in such questions, first look for a perfect square or verify that the discriminant \(D=b^2-4ac\) is zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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