Question

Question 12
Find the zeroes of the polynomial $p\left(x\right)=(x-2{)}^2–(x+2{)}^2$

Answer 1

$p\left(x\right)=(x-2{)}^2–(x+2{)}^2$
For zeroes of polynomial, put p(x) = 0.
$(x–2{)}^2–(x+2{)}^2=0$
$\Rightarrow (x–2+x+2)(x–2–x–2)=0$ [ Using identity, $a^2–b^2=(a–b)(a+b)$ ]
$\Rightarrow \left(2x\right)(-4)=0$
$\Rightarrow -8x=0$
$\Rightarrow x=0$ $[\because -8\ne 0]$
Hence, zero of the polynomial p(x) is 0.