Please answer the question in the attachment
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Answer:
Step-by-step explanation:
We know that if m and n are the roots of a quadratic equation ax
2
+bx+c=0, the sum of the roots is m+n=−
a
b
and the product of the roots is mn=
a
c
.
Here, the given quadratic equation x
2
−6x+2=0 is in the form ax
2
+bx+c=0 where a=1,b=−6 and c=2.
The sum of the roots is:
m+n=−
a
b
=−
1
(−6)
=6
The product of the roots is
a
c
that is:
mn=
a
c
=
1
2
=2
Now,
m
3
n
2
+n
3
m
2
=m
2
n
2
(m+n)=(mn)
2
(m+n)=2
2
×6=4×6=24
Hence, the value of m
3
n
2
+n
3
m
2
=24.
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