This is the basic and conceptual question from polynomials in which we have been asked to find all the zeroes of the polynomial if (3+√2) and (3-√2) are the zeroes of the polynomial (2x^4-11x³+7x²+13x-7).

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2B, question no 19

Let f(x)=2x^4−11x³+7x²+13x−7

Given : (3+√2) and (3−√2) are the zeroes of f(x)

So (x−(3+√2)) and (x−(3−√2)) are factors of f(x)

and (x−(3+√2))(x−(3−√2))=x²−6x+7 is a factor of f(x)

Divide f(x) by x²−6x+7 we get

set f(x)=0

2x^4−11x³+7x²+13x−7=0

(x²−6x+7)(2x²+x−1)=0

(x−(3−(√2))(x−(3+√2))(2x−1)(x+1)=0

x=3−√2 or x=3+√2 or x=1/2 or x=−1

hence all the zeros of the given polynomial are (−3−√2), (−3+√2), 1/2and −1.