If the product of the roots of the equation \(x^2-2(a-2)x+a^2-9=0\) is zero, what are the values of \(a\)?
Answer and explanation
Correct answer: 3 and −3
By Vieta’s formula, the product of the roots of \(Ax^2+Bx+C=0\) is \(C/A\). Here, \(A=1\) and \(C=a^2-9\), so the product of the roots is \(a^2-9\). Setting it equal to zero gives \(a^2-9=0\), or \(a^2=9\), hence \(a=3\) or \(a=-3\). Option A is incorrect because \(a^2=9\) does not give 0 and 9 as the values of \(a\). Exam tip: Use Vieta’s formulas directly when only the sum or product of roots is given.
Frequently asked questions
What is the correct answer to this question?
3 and −3
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 \(C=a^2-9\), so the product of the roots is \(a^2-9\). Setting it equal to zero gives \(a^2-9=0\), or \(a^2=9\), hence \(a=3\) or \(a=-3\). Option A is incorrect because \(a^2=9\) does not give 0 and 9 as the values of \(a\). Exam tip: Use Vieta’s formulas directly when only the sum or product of roots is given.
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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