(C) Given that $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$. By the factor theorem,we can write: $f(x) = (x - 2)(x - 3)(x -

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(C) Given that $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$. By the factor theorem,we can write: $f(x) = (x - 2)(x - 3)(x - 6)$ Expanding the right side: $f(x) = (x^2 - 5x + 6)(x - 6)$ $f(x) = x^3 - 6x^2 - 5x^2 + 30x + 6x - 36$ $f(x) = x^3 - 11x^2 + 36x - 36$ Comparing this with $f(x) = x^3 + ax^2 + bx + c$,we get: $a = -11$,$b = 36$,$c = -36$ Now,calculating $a - c$: $a - c = -11 - (-36) = -11 + 36 = 25$

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

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If $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$,where $a, b, c \in \mathbb{C}$. Then,the value of $a - c$ is

AP EAMCET 2022 All AP EAMCET

A
$-11$
B
$36$
C
$25$
D
$11$

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