If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-8x+12=0\), what is the value of \(\alpha^2\beta^2\)?

144

For a quadratic equation \(ax^2+bx+c=0\), the product of its roots is \(\alpha\beta=\frac{c}{a}\). Here, \(a=1\) and \(c=12\), so \(\alpha\beta=12\). Therefore, \(\alpha^2\beta^2=(\alpha\beta)^2=12^2=144\). Option 12 is only the value of \(\alpha\beta\), not its square. Exam tip: Remember that the sum and product of the roots are \(-\frac{b}{a}\) and \(\frac{c}{a}\), respectively.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.