Question

Find the value of P(x) = x^3-2x^2+3x+1 at x = 2- root 3.​

Answer 1

Step-by-step explanation:

Given:-

P(x) = x^3-2x^2+3x+1

To find:-

Find the value of P(x) = x^3-2x^2+3x+1

at x = 2- √3.

Solution:-

Given Cubic polynomial is x^3-2x^2+3x+1

P(x) = x^3-2x^2+3x+1

Put x = 2-√3 in the given P(x) then

=>P(2-√3)

=>(2-√3)^3 - 2(2-√3)^2 + 3(2-√3) + 1

We know that

(a-b)^3=a^3-3a^2b+3ab^2-b^3

(a-b)^2=a^2 - 2ab +b^2

(2-√3)^3

=2^3 -3(2)^2(√3)+3(2)(√3)^2-(√3)^3

=8-12√3+18-3√3

=26-15√3

(2-√3)^3= 26-15√3

(2-√3)^2

=2^2-2(2)(√3)+(√3)^2

=4-4√3+3

(2-√3)^2=7-4√3

now,

(2-√3)^3 - 2(2-√3)^2 + 3(2-√3) + 1

=(26-15√3)-2(7-4√3)+3(2-√3)+1

=> 26 -15√3 -14 + 8√3+6-3√3+1

=> (26-14+6+1) +(-15√3+8√3-3√3)

=> (33-14)+(8√3-18√3)

= (19) +(-10√3)

=> 19 -10√3

Answer:-

The value of P(x) at x=2-√3 for the given problem is 19 - 10√3