F.4 maths(polynomial)

2013-03-03 9:59 pm

1: Let f(x)= x^n +2x+3,where n is a positive odd integer.
a)Find the remainder when f(x) is divided by x+1.
b)Using the result of (a), or otherwise,find the remainder when f(x) is divided by x^2 -1.

2: For two distinct real numbers p and q,it is known that the polynomials 2x^2 +qx+p have a common factor x-r.
a) Find the value of r.
b) Given that x-1 is a factor of 2x^2 +3x-5,write another polynomial which has a
factor of x-1

回答 (1)

麻辣

2013-03-04 2:55 am

✔ 最佳答案

1:Let f(x)= x^n +2x+3,where n is a positive odd integer.(a)Find the remainder when f(x) is divided by x+1.f(-1)=(-1)^n+2*(-1)+3=-1-2+3=0r=0.......ans
(b)Using the result of (a), or otherwise,find the remainder when f(x) is divided by x^2 -1.f(x)=(x^2-1)*Q(x)+(ax+b)f(-1)=-a+b=0 => a=bf(1)=a+b=1+2+3=6 => 2a=6 => a=b=3R(x)=ax+b=3(x+1)........ans
2: For two distinct real numbers p and q,it is known that the polynomials f(x)=2x^2+qx+p have a common factor x-r.(a) Find the value of r.f(r)=2r^2+qr+p=0r=[-q+-√(q^2-8p)]/4.......ans (b) Given that x-1 is a factor of f(x)=2x^2 +3x-5,write another polynomial which has a factor of x-1f(1)=2+3-5=0g(x)=2x^2-5x+3.......ansg(1)=2-5+3=0

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