Question

Find the zero of the polynomial in each of the following.

a. $p\left(x\right)=3x-2$
b. $3x$
c. $ax,a\ne 0$
d. $cx+d,c\ne 0,c,d$ are real numbers.

Answer 1

• In the given question we have four polynomials where we have to find the zeros of each polynomial.

a. Zero of polynomial 𝑝(𝑥)=3𝑥−2 is
$p\left(x\right)=3x-2=0$.
$3x=2$
$x=23$
Hence, $\frac{2}{3}$ is the zero of the polynomial $p\left(x\right)=3x-2.$

b. Zero of the polynomial 3𝑥 is
$p\left(x\right)=3x=0$.
$x=\frac{0}{3}=0.$
Hence, 0 is the zero of 3x.

c. Zero of the polynomial 𝑎𝑥, 𝑎≠0 is
$p\left(x\right)=ax$, where $a\ne 0$.
$ax=0$
$x=\frac{0}{a}=0$
Hence, 0 is the zero of ax.

d.Zero of the polynomial $cx+d,c\ne 0,c,d$
𝑎𝑟𝑒 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 is
$cx+d,(c\ne 0)\Rightarrow cx=-d.$
$x=-dc.$
Hence, $\frac{-d}{c}$ is the zero of $cx+d$