Question

Find the relation between the root and coefficient of x³ - 6x² + 11x - 6.

Answer 1

\(x^3 - 6x^2 + 11x -6 = 0\)

Let roots are \(\alpha, \beta\) and \(\gamma\).

Then sum of roots = \(\alpha + \beta + \gamma = \frac{-b}a = \frac{-(-6)}1 = 6\)

Sum of products of two roots = \(\alpha\beta + \beta\gamma + \alpha\gamma = \frac ca = \frac{11}1 = 11\)

Product of roots = \(\alpha \beta\gamma = \frac{-d}a = \frac{-(-6)}1 = 6\).