Question

If the zeroes of the polynomial $x^3-3x^2+x+1$ are $a-b,a,a+b$ find $a$ and $b$. [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Given polynomial is,

$x^3-3x^2+x+1$

Sum of zeroes = $\frac{-b}{a}$

$\Rightarrow (a-b)+a+(a+b)=3$ [ $\because \frac{-b}{a}=3$]

$\Rightarrow 3a=3$

$\Rightarrow a=1$

Now product of zeroes = $\frac{-d}{a}$

$\Rightarrow (a-b)\times a\times (a+b)$ = $\frac{-d}{a}$

$\Rightarrow (1-b)\times 1\times (1+b)=-1$ [ $\because \frac{-d}{a}=-1$]

$\Rightarrow 1-b^2=-1$

$\Rightarrow b=\pm \sqrt{2}$