Ifa and B are the zeros of the polynomial 25x2 - 16, then a2 + B2 is:
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Given
25x
2
+25x+5
α and β the zeros of the polynomial
α+β=
a
−b
=
25
−25
=−1
αβ=
a
c
=
25
5
=
5
1
(α+β)
2
=(−1)
2
α
2
+2αβ+β
2
+2(
5
1
)=1
α
2
+β
2
+
5
2
=1
α
2
+β
2
=1−
5
2
=
5
3
α
2
1
+
β
2
1
=
α
2
β
2
α
2
+β
2
=
(αβ)
2
α
2
+β
2
=
(
5
1
)
2
(
5
3
)
=
25
1
5
3
=
5
3
×25=15
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