If the roots of \(x^2-2mx+64=0\) are equal, what are the possible values of \(m\)?
Answer and explanation
Correct answer: m = \pm 8
For equal roots the discriminant must be zero: \(D=0\). In the given equation \(a=1,\ b=-2m,\ c=64\). So \(D=b^2-4ac=(-2m)^2-4\cdot1\cdot64=4m^2-256\). Setting \(D=0\) gives \(4m^2-256=0\Rightarrow m^2=64\Rightarrow m=\pm8\). Thus \(m=\pm8\) is correct. The option \(m=\pm16\) is incorrect because it yields a nonzero discriminant (roots are not equal). Exam tip: always compute \(b^2-4ac\) first for equal/distinct roots and solve the resulting equation for the parameter.
Frequently asked questions
What is the correct answer to this question?
m = \pm 8
Why is this the correct answer?
For equal roots the discriminant must be zero: \(D=0\). In the given equation \(a=1,\ b=-2m,\ c=64\). So \(D=b^2-4ac=(-2m)^2-4\cdot1\cdot64=4m^2-256\). Setting \(D=0\) gives \(4m^2-256=0\Rightarrow m^2=64\Rightarrow m=\pm8\). Thus \(m=\pm8\) is correct. The option \(m=\pm16\) is incorrect because it yields a nonzero discriminant (roots are not equal). Exam tip: always compute \(b^2-4ac\) first for equal/distinct roots and solve the resulting equation for the parameter.
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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