Can the sum of the roots of ((m+1)x^2-2(m-1)x+(m-3)=0) be (2)?
Answer and explanation
Correct answer: No, no value
For a quadratic equation \\(Ax^2+Bx+C=0\\), the sum of the roots is \\(-B/A\\), provided \\(A\\ne0\\). Here, \\(A=m+1\\) and \\(B=-2(m-1)\\), so the sum is \\(2(m-1)/(m+1)\\). To make this sum equal to 2, solve \\(2(m-1)/(m+1)=2\\), with the necessary restriction \\(m\\ne-1\\).
Dividing by 2 and multiplying by \\(m+1\\) gives \\(m-1=m+1\\). Subtracting \\(m\\) from both sides gives \\(-1=1\\), which is impossible. The excluded value \\(m=-1\\) makes the quadratic coefficient zero, so it cannot provide a quadratic equation anyway. Therefore no permitted value of \\(m\\) works, and option D is correct.
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What is the correct answer to this question?
No, no value
Why is this the correct answer?
For a quadratic equation \\(Ax^2+Bx+C=0\\), the sum of the roots is \\(-B/A\\), provided \\(A\\ne0\\). Here, \\(A=m+1\\) and \\(B=-2(m-1)\\), so the sum is \\(2(m-1)/(m+1)\\). To make this sum equal to 2, solve \\(2(m-1)/(m+1)=2\\), with the necessary restriction \\(m\\ne-1\\).
Dividing by 2 and multiplying by \\(m+1\\) gives \\(m-1=m+1\\). Subtracting \\(m\\) from both sides gives \\(-1=1\\), which is impossible. The excluded value \\(m=-1\\) makes the quadratic coefficient zero, so it cannot provide a quadratic equation anyway. Therefore no permitted value of \\(m\\) works, and option D is correct.
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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