if m and n are the zeros of the polynomial x2 +x-2 then find the value of the m3n +n3m
Answers
Answered by
2
Answer:
given polynomial is
x² + x -2 = 0
zeroes are m and n.
sum of zeroes = -b/a
=> m + n = -1/1 = -1
and
product of zeroes = c/a
=> mn = -2/1
=> mn = -2
now,
m³n + n³m
= mn( m² + n²)
= -2{ ( m + n)² - 2mn}
= -2{ (-1)² -2 × ( -2)}
= -2{ 1 +4}
= -2 × 5
= -10.
Answered by
1
Step-by-step explanation:
ANSWERANSWER
n
m
+
m
n
=
mn
m
2
+n
2
=
mn
(m+n)
2
−mn
⇒
n
m
+
m
n
=
mn
(m+n)
2
−1.....(1)
Given that m and n are the zeroes of the polynomial 3x
2
+11x−4.
Therefore,
Sum of zeroes =m+n=−
a
b
=−
3
11
Product of zeroes =mn=
a
c
=
3
−4
∴
n
m
+
m
n
=
(
3
−4
)
(
3
−11
)
2
−1=−
16
121
−1=−
16
137
Hence the value of
n
m
+
m
n
wil be −
16
137
.
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