Find the zeroes of the quadratic polynomial 6
2
- 3 -7x and verify the relation
between the zeroes and their coefficients
Answers
Answer:
We have,
f(x)=6x
2
−3
→ f(X)=(
6
x)
2
−(
3
)
2
→ f(x)=(
6
x−
3
)(
6
x+
3
)
The zeros of f(x) are given by f(x) =0
ie., (
6
x−
3
)(
6
x+
3
)=0
⇒
6
x−
3
=0 or,
6
x+
3
=0
⇒ x=
6
3
or, x=
6
−
3
⇒ x=
2
1
or x=−
2
1
Hence, the zeros of f(x)=6x
2
−3 are: α=
2
1
= and β=−
2
1
Now,
Sum of the zeros = α+β=
2
1
+(−
2
1
)=0
Sum of the zeros = -
Coefficient of x
2
Coefficient of x
∴ -
Coefficient of x
2
Coefficient of x
=−
6
0
=0
Also,
Product of the zeros = αβ =
2
1
×
2
−1
=
2
−1
and,
∴ Product of the zeros=
Coefficient of x
2
Constant term
=
6
−3
=
2
−1
Hence verified.
hope it will help
Answer:
ANSWER
We have,
f(x)=6x
2
−3
→ f(X)=(
6
x)
2
−(
3
)
2
→ f(x)=(
6
x−
3
)(
6
x+
3
)
The zeros of f(x) are given by f(x) =0
ie., (
6
x−
3
)(
6
x+
3
)=0
⇒
6
x−
3
=0 or,
6
x+
3
=0
⇒ x=
6
3
or, x=
6
−
3
⇒ x=
2
1
or x=−
2
1
Hence, the zeros of f(x)=6x
2
−3 are: α=
2
1
= and β=−
2
1
Now,
Sum of the zeros = α+β=
2
1
+(−
2
1
)=0
Sum of the zeros = -
Coefficient of x
2
Coefficient of x
∴ -
Coefficient of x
2
Coefficient of x
=−
6
0
=0
Also,
Product of the zeros = αβ =
2
1
×
2
−1
=
2
−1
and,
∴ Product of the zeros=
Coefficient of x
2
Constant term
=
6
−3
=
2
−1
Hence verified.