If a = 3 is substituted, what type of statement does (a − 3)x² + (a² − 9)x + 11 = 0 become?
Answer and explanation
Correct answer: Contradictory statement
Substituting a = 3 gives a − 3 = 0 and a² − 9 = 9 − 9 = 0. Therefore, the equation reduces to 11 = 0, which is a false and contradictory statement, so it has no solution. Exam tip: When the coefficients of the variable terms become zero, check whether the remaining constant statement is true or false; a false statement has no solution.
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What is the correct answer to this question?
Contradictory statement
Why is this the correct answer?
Substituting a = 3 gives a − 3 = 0 and a² − 9 = 9 − 9 = 0. Therefore, the equation reduces to 11 = 0, which is a false and contradictory statement, so it has no solution. Exam tip: When the coefficients of the variable terms become zero, check whether the remaining constant statement is true or false; a false statement has no solution.
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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