If the product of the roots of the equation \(x^2-2(a+1)x+a^2-1=0\) is zero, which values of \(a\) are possible?
Answer and explanation
Correct answer: 1 or -1
By Vieta’s formula, the product of the roots of \(Ax^2+Bx+C=0\) is \(C/A\). Here, \(A=1\) and \(C=a^2-1\), so the product of the roots is \(a^2-1\). Setting it equal to zero gives \(a^2-1=0\), or \(a^2=1\), hence \(a=1\) or \(a=-1\). Therefore, option A is correct. Exam tip: Use Vieta’s formulas directly when a question asks for the sum or product of roots, and remember to consider both values obtained after solving the parameter equation.
Frequently asked questions
What is the correct answer to this question?
1 or -1
Why is this the correct answer?
By Vieta’s formula, the product of the roots of \(Ax^2+Bx+C=0\) is \(C/A\). Here, \(A=1\) and \(C=a^2-1\), so the product of the roots is \(a^2-1\). Setting it equal to zero gives \(a^2-1=0\), or \(a^2=1\), hence \(a=1\) or \(a=-1\). Therefore, option A is correct. Exam tip: Use Vieta’s formulas directly when a question asks for the sum or product of roots, and remember to consider both values obtained after solving the parameter equation.
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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