find the zero of x² -2x-8 also verify the relationship between the zero and the coefficient of the polynomial
Answers
Answered by
0
Step-by-step explanation:
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x ( x + 2 ) - 4 ( x + 2 ) = 0
( x + 2 ) ( x - 4 ) = 0
x + 2 = 0
x = - 2
x - 4 = 0
x = 4
The zeroes are - 2 and 4.
Let,
α = - 2
β = 4
x² - 2x - 8 = 0
Here,
a = 1
b = - 2
c = - 8
α + β = - b / a
- 2 + 4 = - ( - 2 ) / 1
2 = 2
αβ = c / a
- 2 ( 4 ) = - 8 / 1
- 8 = - 8
Hence,
the relationship between the zero and the coefficient of the polynomial is verified.
Answered by
1
Given polynomial is x
2
−3
Here, a=1,b=0 and c=−3
x
2
−3=(x−
3
)(x−
3
)
So, the value of x
2
−3 is zero when x=
3
or x=−
3
Threrfore , thr zeroes of x
2
−3 are
3
and −
3
.
Now, sum of zeroes =
3
−
3
=0=
1
0
=
a
−b
product of zeroes =(
3
)(−
3
)=−3=
1
−3
=
a
c
I hope it helps you
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