Question 12
Find the zeroes of the polynomial p(x)=(x−2)2–(x+2)2
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Solution
p(x)=(x−2)2–(x+2)2
For zeroes of polynomial, put p(x) = 0. (x–2)2–(x+2)2=0 ⇒(x–2+x+2)(x–2–x–2)=0 [ Using identity, a2–b2=(a–b)(a+b) ] ⇒(2x)(−4)=0 ⇒−8x=0 ⇒x=0[∵−8≠0]
Hence, zero of the polynomial p(x) is 0.