Write a second degree polynomial p(x) in which \(p(\sqrt{2}+1)=p(\sqr

1.	Write a second degree polynomial p(x) in which \(p(\sqrt{2}+1)=p(\sqrt{2}-1)=0\)
Answer» If \(p(\sqrt{2}+1)=0\), then x\(-(\sqrt{2}+1)\) is a factor. If \(p(\sqrt{2}-1)=0\), then x\(-(\sqrt{2}-1)\) is a factor. p(x) = [x-(√2+1)][x-(√2-1)] = [x-(√2-1)][x-(√2+1)] = (x-√2)² - 1 = x² - 2√2 x+2-1 = x²-2√2x+1

Write a second degree polynomial p(x) in which \(p(\sqrt{2}+1)=p(\sqrt{2}-1)=0\)

Answer»

If \(p(\sqrt{2}+1)=0\), then x\(-(\sqrt{2}+1)\) is a factor.

If \(p(\sqrt{2}-1)=0\), then x\(-(\sqrt{2}-1)\) is a factor.

p(x) = [x-(√2+1)][x-(√2-1)]

= [x-(√2-1)][x-(√2+1)]

= (x-√2)² - 1 = x² - 2√2 x+2-1

= x²-2√2x+1

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Write a second degree polynomial p(x) in which \(p(\sqrt{2}+1)=p(\sqrt{2}-1)=0\)

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