Find all the zeros of the polynomialx^4-3x^3-5x^2+22x-14 if two of the

1.	Find all the zeros of the polynomialx^4-3x^3-5x^2+22x-14 if two of the zeros are√7 and -√7.
Answer» Since {tex}\\sqrt 7{/tex}\xa0and {tex}-\\sqrt 7{/tex}\xa0are the zeroes of the given polynomial.This means (x−{tex}\\sqrt 7{/tex}) and (x+{tex}\\sqrt 7{/tex}) are the factors of the given polynomial.So dividing p(x) = x4−3x3−5x2+21x−14 by (x−{tex}\\sqrt 7 {/tex})(x+{tex}\\sqrt 7{/tex}) i.e. x2−7using long division method we get;\xa0So x2−3x+2 is the factor of the given polynomial. To find other zeroes equate it to 0 we get;x2−3x+2 =0=>x2−2x-x+2 =0=> x(x-2)-1(x-2)=0=> (x-2)(x-1)=0=> x= 1,2

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