Question

State whether the following statement is True or False

Zeroes of $x^2-5x$are 0 and -5

• A. True
• B. False

Answer 1

The correct option is B False

Checking if zeroes of $x^2-5x$ are 0 and -5:

Zeroes of the polynomial:- A real number $‘a’$ is zero of the polynomial $p\left(x\right)ifp\left(a\right)=0$.

Let, $p\left(x\right)=x^2-5x$

Step 1. Checking if 0 is a zero of $x^2-5x$:

Putting $x=0$ in $p\left(x\right)$ , we get

$$\begin{gathered} p\left(0\right)={\left(0\right)}^2-5\left(0\right) \\ \Rightarrow p\left(0\right)=0-0 \\ \Rightarrow p\left(0\right)=0 \end{gathered}$$

So, 0 is zero of the given polynomial.

Step 2. Checking if -5 is a zero of $x^2-5x$:

Putting $x=-5$ in $p\left(x\right)$ , we get

$$\begin{gathered} p(-5)={(-5)}^2-5(-5) \\ \Rightarrow p(-5)=25-(-25) \\ \Rightarrow p(-5)=25+25 \\ \Rightarrow p(-5)=50 \end{gathered}$$

So, -5 is not a zero of the given polynomial.

Hence, the given statement is false.