if alpha and beta are the zeros of the polynomial 3x^2+5x-2 then form a quadratic polynomial whose zeros are 2 alpha and 2 beta
Answers
Answered by
2
Answer:
Given a quadratic polynomial
a
x
2
+
b
x
+
c
sum of its zeroes
α
and
β
is
−
b
a
and product of zeroes is
c
a
. Further if sum of zeroes is
s
and product of zeroes is
p
, then quadratic polynomial is
x
2
−
s
x
+
p
.
Hence for
3
x
2
+
5
x
−
2
we have
α
+
β
=
−
5
3
and
α
β
=
−
2
3
We now desire quadratic polynomial whose zeroes are
2
α
and
2
β
As sum of roots is
2
α
+
2
β
=
2
(
α
+
β
)
=
2
×
−
5
3
=
−
10
3
and product of roots is
2
α
×
2
β
=
4
α
β
=
4
×
−
2
3
=
−
8
3
and quadratic polynomial is
x
2
+
10
3
x
−
8
3
as zeroes are not affected by multiplying each term of polynomial by a constant,
we can say quadratic polynomial is
3
x
2
+
10
x
−
8
Answered by
1
Answer:
3x^2+6x-x-2
3x(x+2) -1(x+2)
(3x-1) (x+2)
α=1/3 β = -2
2α=2/3 and 2β=-4
(x-2/3) (x+4)
x^2+4x-2/3x-8/3
3x^2+10x-8 is a polynomial
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