if alpha and beta are zeroes of quadratic polynomial x²-4x+3 then find the value of alpha beta-alpha beta
Answers
Answer:
Correct option is
D
3x
2
−16x+16
Since α and β are the zeros of the quadratic polynomial x
2
+4x+3
Then, α+β=−4,αβ=3
Now, the of sum of the zeros of new polynomial is
=1+
α
β
+1+
β
α
=
αβ
αβ+β
2
+αβ+α
2
=
αβ
α
2
+β
2
+2αβ
=
αβ
(α+β)
2
=
3
(−4)
2
=
3
16
Also, Product of the zeros of new polynomial is
=2+
αβ
α
2
+β
2
=
αβ
2αβ+α
2
+β
2
=
αβ
(α+β)
2
=
3
(−4)
2
=
3
16
Therefore, the required polynomial is
k×[x
2
−(sum of the zeros)x+product of zeros]
⇒k×[x
2
−
3
16
x+
3
16
]
⇒3×(x
2
−
3
16
x+
3
16
) (if k=3)
⇒3x
2
−16x+16
Answer:
if alpha and beta are zeroes of quadratic polynomial x²-4x+3 then find the value of alpha beta-alpha beta
Step-by-step explanation:
x2-4x+3
ac=3
x2-3x-1x+3
x(x-3) -1(x-3)
(x-3) (x-1)
x-3=0 x-1=0
=3 x=1
∝=3 and β=1