If α & β are the zeroes of the quadratic polynomial f(x) =x² -3x-2, then how do you find a quadratic polynomial whose zeroes are 1/ α and 1/ β?
Answers
Answer:
Since α and β are the zeros of the quadratic polynomial f(x) = x2 − 1
The roots are α and β
α
+
β
=
-coefficient of x
coefficient of
x
2
α+β=-coefficient of xcoefficient of x2
α
+
β
=
0
1
α+β=01
α
+
β
=
0
α+β=0
α
β
=
constant term
coefficient of
x
2
αβ=constant termcoefficient of x2
α
β
=
−
1
1
αβ=-11
α
β
=
−
1
αβ=-1
Let S and P denote respectively the sum and product of zeros of the required polynomial. Then,
S
=
2
α
β
+
2
β
α
S=2αβ+2βα
Taking least common factor we get,
S
=
2
α
2
+
2
β
2
α
β
S=2α2+2β2αβ
S
=
2
(
α
2
+
β
2
)
α
β
S=2(α2+β2)αβ
S
=
2
[
(
α
+
β
)
−
2
α
β
]
α
β
S=2[(α+β)-2αβ]αβ
S
=
2
[
(
0
)
−
2
(
−
1
)
]
−
1
S=2[(0)-2(-1)]-1
S
=
2
[
−
2
(
−
1
)
]
−
1
S=2[-2(-1)]-1
S
=
2
×
2
−
1
S=2×2-1
S
=
4
−
1
S=4-1
S = -4
P
=
2
α
β
×
2
β
α
P=2αβ×2βα
P = 4
Hence, the required polynomial f(x) is given by,
f(x) = k(x2 - Sx + P)
f(x) = k(x2 -(-4)x + 4)
f(x) = k(x2 +4x +4)
Hence, required equation is f(x) = k(x2 +4x +4) Where k is any non zero real number.
PLEASE MAKE ME BRAINLIEST AND FOLLOW ME,!
Answer:
see the attachment for answer
Step-by-step explanation:
plzz mark as brainlist.. if you get the right answer
