find the zeros of x^3+2x^2+3x+5
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Answer:
Answer
2x
2
−3x+5=0
Sum of the roots =
a
−b
=
2
3
Product of the roots =
a
c
=
2
5
Let p+q=
2
3
,pq=
2
5
ax
2
+bx+2=0
Let
p
1
,
q
1
be the roots
The roots are reciprocal, therefore,
pq
p+q
=
2
3
÷
2
5
=
5
3
=
a
−b
∴−5b=3a
pq
1
=
a
2
=
5
2
∴a=5,b=−3
The new qudratic equation is :5x
2
−3x+2=0
Verification:
Sum=
5
3
,Product=
5
2
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