If the product of the roots of the equation \(x^2-2(a-3)x+a^2-16=0\) is zero, what are the values of \(a\)?
Answer and explanation
Correct answer: \(4\) and \(-4\)
For a quadratic equation \(Ax^2+Bx+C=0\), the product of its roots is \(C/A\). Here, \(A=1\) and \(C=a^2-16\), so the product of the roots is \(a^2-16\). Setting it equal to zero gives \(a^2-16=0\), or \(a^2=16\), hence \(a=4\) or \(a=-4\). Therefore, option A is correct. In exams, remember that the sum and product of roots are \(-B/A\) and \(C/A\), respectively.
Frequently asked questions
What is the correct answer to this question?
\(4\) and \(-4\)
Why is this the correct answer?
For a quadratic equation \(Ax^2+Bx+C=0\), the product of its roots is \(C/A\). Here, \(A=1\) and \(C=a^2-16\), so the product of the roots is \(a^2-16\). Setting it equal to zero gives \(a^2-16=0\), or \(a^2=16\), hence \(a=4\) or \(a=-4\). Therefore, option A is correct. In exams, remember that the sum and product of roots are \(-B/A\) and \(C/A\), respectively.
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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