15)p (x) = x2 - 4x + 4 a) Prove that (x - 2) is a factor of p (x) - Maths - Polynomials

Question

15)p (x) = x2 - 4x + 4
a) Prove that (x - 2) is a factor of p (x)
b) Prove that for any number x, p (x) is always non negative
c) Find the number a and b such that p(a) = p (b)

Shruti Tyagi · Accepted Answer

Dear student,
p(x)=x2-4x+4a) since (x-2) is a factor of p(x)then p(2)=22-8+4=4-8+4=8-8=0as p(2)=0 therefore, (x-2) is a factor of p(x)b) p(x)=x2-4x+4=x2-2×x×2+22=x-22               --[using (x-y)2=x2+y2-2xy]which is a perfect square
thus p(x) is always non negative
c) We have, p(a)=p(b)⇒a2-4a+4=b2-4b+4⇒a-22=(b-2)2 we can put a=6 and b=-2then (6-2)2=-2-22⇒42=(-4)2⇒16=16Similarly we can find more values of a and b
Regards

15)p (x) = x2 - 4x + 4 a) Prove that (x - 2) is a factor of p (x) b) Prove that for any number x, p (x) is always non negative c) Find the number a and b such that p(a) = p (b)

15)p (x) = x2 - 4x + 4
a) Prove that (x - 2) is a factor of p (x)
b) Prove that for any number x, p (x) is always non negative
c) Find the number a and b such that p(a) = p (b)