Question

If $a,a+b,a+2b$ are zeroes of the cubic polynomial $x^3-6x^2+3x+10$ , then $a+b=$________.

Answer 1

Let f(x) = $x^3-6x^2+3x+10$
Given, the zeroes of f(x) = $a,a+b,a+2b$

$\therefore$ Sum of zeroes $=a+a+b+a+2b$

$\Rightarrow \frac{-b}{a}=a+a+b+a+2b$ ($\because$ sum of zeroes $=\frac{-coefficientof{x}^2}{coefficientof{x}^3}$ )

$\therefore \frac{-(-6)}{1}=3a+3b$

$\Rightarrow 6=3(a+b)$

$\Rightarrow \frac{6}{3}=a+b$

$\Rightarrow 2=a+b$

Hence, if $a,a+b,a+2b$ are the zeroes of the cubic polynomial $x^3-6x^2+3x+10$ , then $a+b=2$ .