Question

List the multiplicities of the zeroes of the polynomial $P\left(x\right)=x^2-14x+49$

• A. $x=5$ is a zero of multiplicity $3$.
• B. $x=7$ is a zero of multiplicity $2$.
• C. $x=6$ is a zero of multiplicity $1$.
• D. None of these

Answer 1

Answer: (B)

$x=7$ is a zero of multiplicity $2$.

Given, $x^2-14x+49$

$\Rightarrow x^2-7x-7x+49$

$\Rightarrow x(x-7)-7(x-7)$

$\Rightarrow (x-7{)}^2$

So, $x=7$ is a zero of multiplicity $2$.