If \\(a=-1\\) is substituted in the equation \\((a+1)x^2+(a^2-1)x+2=0\\), what type of result is obtained?
Answer and explanation
Correct answer: Contradictory statement
Substituting \\(a=-1\\) gives \\(a+1=0\\) and \\(a^2-1=1-1=0\\). Hence the equation becomes \\(0x^2+0x+2=0\\), or \\(2=0\\). This is a false, contradictory statement and has no solution. It is not a linear equation because the coefficient of \\(x\\) is also zero. In parameter-based equations, first check the coefficients of \\(x^2\\), \\(x\\), and the constant term separately.
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What is the correct answer to this question?
Contradictory statement
Why is this the correct answer?
Substituting \\(a=-1\\) gives \\(a+1=0\\) and \\(a^2-1=1-1=0\\). Hence the equation becomes \\(0x^2+0x+2=0\\), or \\(2=0\\). This is a false, contradictory statement and has no solution. It is not a linear equation because the coefficient of \\(x\\) is also zero. In parameter-based equations, first check the coefficients of \\(x^2\\), \\(x\\), and the constant term separately.
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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