Q. 254.7( 6 Votes )

Find a seco

Answer :

Given: p(1 + √3) = 0, p(1 – √3) = 0


Concept Used:


A second–degree polynomial is given by,


p(x) = ax2 + bx + c


Explanation:


Since we know that p(1 + √3) = 0


if x = 1 + √3 is substituted in p(x) then it satisfies the equation


x – (1 + √3) = 0 , and ((x – 1) – √3) is one factor of p(x)


And p(1 – √3) = 0 is given


if x = 1 – √3 is substituted in p(x) then it satisfies the equation


x – (1 – √3) = 0, and ((x – 1) + √3) is one factor of p(x)


since, ((x – 1) – √3) and ((x – 1) + √3) are the factors of p(x), it can be written as follows


p(x) = ((x – 1) – √3)((x – 1) + √3)


p(x) = (x – 1 – √3)(x – 1 + √3)


p(x) = x2 – x + √3x –x + 1 – √3 – √3x + √3 – 3


p(x) = x2 – 2x – 2


x2 – 2x – 2 is the second degree polynomial which satisfies p(1 + √3) = 0 and p(1 – √3) = 0.


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