If \(a=2\), what type of statement does \((a-2)x^2+(a^2-4)x+5=0\) become?
Answer and explanation
Correct answer: Contradictory statement (no solution)
Substituting \(a=2\) gives \((2-2)x^2+(2^2-4)x+5=0\), or \(0x^2+0x+5=0\), which reduces to \(5=0\). This statement is false and is satisfied by no value of \(x\), so it is a contradictory statement. It is not linear because the coefficient of \(x\) is also zero, and it is not always true. Exam tip: After substituting a parameter value, check the highest non-zero power and whether the resulting constant statement is true or false.
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What is the correct answer to this question?
Contradictory statement (no solution)
Why is this the correct answer?
Substituting \(a=2\) gives \((2-2)x^2+(2^2-4)x+5=0\), or \(0x^2+0x+5=0\), which reduces to \(5=0\). This statement is false and is satisfied by no value of \(x\), so it is a contradictory statement. It is not linear because the coefficient of \(x\) is also zero, and it is not always true. Exam tip: After substituting a parameter value, check the highest non-zero power and whether the resulting constant statement is true or false.
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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