If \\(x^2+2(m-2)x+(m^2-3m+4)=0\\) has equal roots, what is the value of \\(m\\)?
Answer and explanation
Correct answer: 0
For a quadratic equation \\(ax^2+bx+c=0\\) to have equal roots, its discriminant must be zero: \\(D=b^2-4ac=0\\). Here, \\(a=1\\), \\(b=2(m-2)\\), and \\(c=m^2-3m+4\\). Therefore, \\(D=4(m-2)^2-4(m^2-3m+4)=-4m\\). Setting \\(D=0\\) gives \\(m=0\\). Exam tip: Whenever equal roots are mentioned, immediately use \\(b^2-4ac=0\\).
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What is the correct answer to this question?
0
Why is this the correct answer?
For a quadratic equation \\(ax^2+bx+c=0\\) to have equal roots, its discriminant must be zero: \\(D=b^2-4ac=0\\). Here, \\(a=1\\), \\(b=2(m-2)\\), and \\(c=m^2-3m+4\\). Therefore, \\(D=4(m-2)^2-4(m^2-3m+4)=-4m\\). Setting \\(D=0\\) gives \\(m=0\\). Exam tip: Whenever equal roots are mentioned, immediately use \\(b^2-4ac=0\\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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