Question

If p(x) = (4x– 5)(4x + 5), what are the zeros of the polynomial?

Answer 1

Statement Problem: If

`p(x)=(4x-5)(4x+5)`

What are the zeros of the polynomial?

Solution:

Zeros of polynomial are the points where the polynomial equals zero on the whole. Zeros of a polynomial are also referred to as the roots of the equation.

Hence, we have;

`(4x-5)(4x+5)=0`

The first zero is;

`\begin{gathered} 4x+5=0 \\ \text{Subtract 5 from both sides;} \\ 4x+5-5=0-5 \\ 4x=-5 \\ \text{Divide both sides by 4;} \\ (4x)/(4)=-(5)/(4) \\ x=-(5)/(4) \end{gathered}`

Similarly, the second zero is;

`\begin{gathered} 4x-5=0 \\ \text{Add 5 to both sides;} \\ 4x-5+5=0+5 \\ 4x=5 \\ Di\text{vide both sides by 4;} \\ (4x)/(4)=(5)/(4) \\ x=(5)/(4) \end{gathered}`

Hence, the zeros of the polynomial are;

`\begin{gathered} x=-(5)/(4) \\ \text{and} \\ x=(5)/(4) \end{gathered}`

CORRECT OPTION: A