if 1 Of The zeros Of The polynomial 3xsq -10x + p is 1/3
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2
Answer:
Step-by-step explanation:
Answer
Let α,β be the zeros of the cubic polynomial
3x
3
−x
2
−3x+1.
1+α+β=−
coefficient of x
3
coefficient of x
2
=
3
−(−1)
=
3
1
⇒α+β=
3
1
−1=
3
(−2)
(i)
Also,
1×α×β=−
a
d
=−
coefficient of x
3
constant term
αβ=−
3
1
⇒α=−
3β
1
Putting the value α=−
3β
1
in equation (i)
⇒
3β
−1
+β=−
3
2
⇒
3β
−1+3β
2
=−
3
2
⇒−1+3β
2
=−2β
⇒3β
2
+2β−1=0
⇒3β
2
+3β−β−1=0
⇒3β(β+1)−1(β+1)=0
⇒(β+1)(3β−1)=0
β=−1,β=
3
1
Now,
⇒α=−
3β
1
Putting the value of β
⇒α=−
3(−1)
1
=
3
1
or,
α=−
3(
3
1
)
1
=−1
Therefore, α,β=(
3
1
,−1)or(−1,
3
1
)
Answered by
1
Step-by-step explanation:
The first person to document zero as a number in its own right was the astronomer and mathematician Brahmagupta in 628 CE.
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