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Byju's Answer
Standard X
Mathematics
Sum and Product of Roots of a Quadratic Equation
Miscellaneous...
Question
Miscellaneous Problem.
Calculate
x
4
1
,
+
x
4
2
where
x
1
a
n
d
x
2
are the roots of the equation
3
x
2
- 5x + 1 = 0.
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Solution
3
x
2
−
5
x
+
1
=
0
(
a
x
2
+
b
x
+
c
=
0
)
Let roots be
x
1
&
x
2
Sum of roots i.e.
x
1
+
x
2
=
−
b
a
=
−
(
−
5
)
3
=
5
3
Products of roots i.e.
x
1
x
2
=
c
a
=
1
3
Now,
(
x
2
1
+
x
2
2
)
=
(
x
1
+
x
2
)
2
−
2
x
1
x
2
=
(
5
/
3
)
2
−
2
(
1
/
3
)
=
19
/
9
x
4
1
+
x
4
2
=
(
x
2
1
+
x
2
2
)
2
−
2
x
2
1
x
2
2
=
(
19
/
9
)
2
−
2
(
1
/
3
)
2
=
343
/
81
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0
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Q.
The equation whose roots are
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