4 If p(x) = x3 6x2 + 11x 1 then ﬁnd p(1),p(2),p(3) Find p(x) p(1),p(x) p(2),p(x) p(3) - Maths - Polynomials

Question

4 If p(x) = x3 −6x2 + 11x−1 then ﬁnd
p(1),p(2),p(3)
Find p(x)−p(1),p(x)−p(2),p(x)−p(3)
Write the solutions of p(x)−p(1) = 0

Lovina Kansal · Accepted Answer

We have, p(x)=x3-6x2+11x-1p(1)=13-6(1)2+11(1)-1=1-6+11-1=5p(2)=23-6(2)2+11(2)-1=8-24+22-1=5p(3)=33-6(3)2+11(3)-1=27-54+33-1=5Now, p(x)-p(1)=x3-6x2+11x-1-5=x3-6x2+11x-6and,p(x)-p(2)=x3-6x2+11x-1-5=x3-6x2+11x-6p(x)-p(3)=x3-6x2+11x-1-5=x3-6x2+11x-6Also,p(x)-p(1)=0⇒x3-6x2+11x-1-5=0⇒x3-6x2+11x-6=0⇒x-1x2-5x+6=0⇒(x-1)x-2x-3=0⇒x-1=0 ,x-2=0 and x-3=0⇒x=1,x=2,x=3

4. If p(x) = x3 −6x2 + 11x−1 then ﬁnd p(1),p(2),p(3) Find p(x)−p(1),p(x)−p(2),p(x)−p(3) . Write the solutions of p(x)−p(1) = 0

4. If p(x) = x3 −6x2 + 11x−1 then ﬁnd p(1),p(2),p(3)
Find p(x)−p(1),p(x)−p(2),p(x)−p(3) .
Write the solutions of p(x)−p(1) = 0