Question

Obtain all other zeroes of the polynomial x⁴-2x³-7x²+8x+12
if two of its zeroes are


$2 \sqrt{2} and - 2 \sqrt{2}$


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Answer 1

Answer:

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product of roots=12

−1×2×α×β=12αβ=−6

sum of the roots=2α+β−1+2

=2α+β=1β=

−α6α−α6=1α2−6

=αα2−α−6=

0α2−3α+2α−6=

0α(α−3)+2(α−3)=

0(α+2)(α−3)=

0α=3,−2

Answer 2

product of roots=12

−1×2×α×β=12αβ=−6

sum of the roots=2α+β−1+2

=2α+β=1β=

−α6α−α6=1α2−6

=αα2−α−6=

0α2−3α+2α−6=

0α(α−3)+2(α−3)=

0(α+2)(α−3)=

0α=3,−2

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