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If are the roots of the equation
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
If
α
,
β
\alpha,\beta
α
,
β
are the roots of the equation
x
2
−
p
x
+
q
=
0
x^2-px+q=0
x
2
−
p
x
+
q
=
0
, find the quadratic equation whose roots are
(
α
2
−
β
2
)
(
α
3
−
β
3
)
(\alpha^2-\beta^2)(\alpha^3-\beta^3)
(
α
2
−
β
2
)
(
α
3
−
β
3
)
and
α
3
β
2
+
α
2
β
3
\alpha^3\beta^2+\alpha^2\beta^3
α
3
β
2
+
α
2
β
3
.
Related theory
Polynomials
Nature and relations of roots
Algebra
Relationship between zeroes and coefficients
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