Question

$\text{What is the zero that is common to the}\text{polynomials}p\left(x\right)=x^2-2x+1\text{and}q\left(x\right)=x^2-3x+2?$

• A. 2
• B. 1
• C. 3
• D. 4

Answer 1

The correct option is B 1

$\text{Let the common zero be a.}$

$\because \text{a is a zero for both the polynomials}p\left(a\right)=0=q\left(a\right)\therefore p\left(a\right)=q\left(a\right)$

$\Rightarrow$ $a^2-2a+1=a^2-3a+2$
$\Rightarrow$ $-2a+1=-3a+2$
$\Rightarrow$ $a=1$

$\therefore \text{The common zero is 1.}$