If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-6x+8=0\), what is the value of \(\alpha^2\beta^2\)?
Answer and explanation
Correct answer: \(64\)
For a quadratic equation \(ax^2+bx+c=0\), the product of the roots is \(\alpha\beta=\frac{c}{a}\). Here, \(a=1\) and \(c=8\), so \(\alpha\beta=8\). Therefore, \(\alpha^2\beta^2=(\alpha\beta)^2=8^2=64\). Option B is only the value of \(\alpha\beta\), not its square. Exam tip: Apply Vieta’s formula directly for the sum and product of the roots.
Frequently asked questions
What is the correct answer to this question?
\(64\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the product of the roots is \(\alpha\beta=\frac{c}{a}\). Here, \(a=1\) and \(c=8\), so \(\alpha\beta=8\). Therefore, \(\alpha^2\beta^2=(\alpha\beta)^2=8^2=64\). Option B is only the value of \(\alpha\beta\), not its square. Exam tip: Apply Vieta’s formula directly for the sum and product of the roots.
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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