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Answers
Answer:
Answer:
polynomial is 2x
4
−11x
3
+7x
2
+13x−7
\text{Sum of the zeros =}3+\sqrt{2}+3-\sqrt{2}=6Sum of the zeros =3+
2
+3−
2
=6
\text{Product of the zeros }Product of the zeros
=(3+\sqrt{2})(3-\sqrt{2})=(3+
2
)(3−
2
)
=3^2-(\sqrt{2})^2=3
2
−(
2
)
2
=9-2=7=9−2=72x^4-11x^3+7x^2+13x-7Given=(3+
2
)(3−
2
)
=3^2-(\sqrt{2})^2=3
2
−(
2
)
2
=9-2=7=9−2=7
\therefore\text{Corresponding factor is }\bf\,x^2-6x+7∴Corresponding factor is x
2
−6x+7
\text{Now,}Now,
2x^4-11x^3+7x^2+13x-7=(x^2-6x+7)(2x^2+px-1)2x
4
−11x
3
+7x
2
+13x−7=(x
2
−6x+7)(2x
2
+px−1)
\text{Equating coefficients of x on both sides we get }Equating coefficients of x on both sides we get
13=6+7p13=6+7p
7p=77p=7
\implies\,p=1⟹p=1
\therefore\text{Other factor is }\,2x^2+x-1∴Other factor is 2x
2
+x−1
2x^2+x-1=(2x-1)(x+1)2x
2
+x−1=(2x−1)(x+1)
\therefore\text{All zeros are }-1,\;\frac{1}{2},\;3+\sqrt{2},\;3-\sqrt{2}∴All zeros are −1,
2
1
,3+
2
,3−Find all the zeros of the polynomial ( 274 – 11x +77 + 13x - 7 ) , it being given that two of its zeros are ( 3 + 2 ) and ( 3-2 ) .
Step-by-step explanation:
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