Statement Problem: If
[tex]p(x)=(4x-5)(4x+5)[/tex]
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;
[tex](4x-5)(4x+5)=0[/tex]
The first zero is;
[tex]\begin{gathered} 4x+5=0 \\ \text{Subtract 5 from both sides;} \\ 4x+5-5=0-5 \\ 4x=-5 \\ \text{Divide both sides by 4;} \\ \frac{4x}{4}=-\frac{5}{4} \\ x=-\frac{5}{4} \end{gathered}[/tex]
Similarly, the second zero is;
[tex]\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;} \\ \frac{4x}{4}=\frac{5}{4} \\ x=\frac{5}{4} \end{gathered}[/tex]
Hence, the zeros of the polynomial are;
[tex]\begin{gathered} x=-\frac{5}{4} \\ \text{and} \\ x=\frac{5}{4} \end{gathered}[/tex]
CORRECT OPTION: A
