if the product of quadratic polynomial is mx2 -6x -8 then find the value of m
Answers
an algebraic expression is compared to zero with an equality sign then this total expression is called algebraic equation.
An algebraic equation having a maximum power of any variable 2, then it is known as a quadratic equation.
The general form of a quadratic equation is as
a
x
2
+
b
x
+
c
=
0
Now if a quadratic equation in one variable after factorisation becomes as
(
x
−
a
)
(
x
−
b
)
=
0
then its roots are
a
,
b
and its factors will be
(
x
−
a
)
and
(
x
−
b
)
where:
Roots are the values which satisfy the above quadratic equation.
Here, we can write,
a
x
2
+
b
x
+
c
=
a
×
(
x
−
α
)
(
x
−
β
)
⟹
a
x
2
+
b
x
+
c
=
a
(
x
(
x
−
α
)
−
β
(
x
−
α
)
)
⟹
a
x
2
+
b
x
+
c
=
a
(
x
2
−
α
x
−
β
x
+
α
β
)
⟹
a
x
2
+
b
x
+
c
=
a
x
2
−
a
(
α
+
β
)
x
+
a
α
β
where:
α
and
β
are the two roots of the equation.
Comparing the coefficients on both sides,
b
=
−
a
(
α
+
β
)
⟹
α
+
β
=
−
b
a
Step-by-step explanation:
If an algebraic expression is compared to zero with an equality sign then this total expression is called algebraic equation.
An algebraic equation having a maximum power of any variable 2, then it is known as a quadratic equation.
The general form of a quadratic equation is as
a
x
2
+
b
x
+
c
=
0
Now if a quadratic equation in one variable after factorisation becomes as
(
x
−
a
)
(
x
−
b
)
=
0
then its roots are
a
,
b
and its factors will be
(
x
−
a
)
and
(
x
−
b
)
where:
Roots are the values which satisfy the above quadratic equation.
Here, we can write,
a
x
2
+
b
x
+
c
=
a
×
(
x
−
α
)
(
x
−
β
)
⟹
a
x
2
+
b
x
+
c
=
a
(
x
(
x
−
α
)
−
β
(
x
−
α
)
)
⟹
a
x
2
+
b
x
+
c
=
a
(
x
2
−
α
x
−
β
x
+
α
β
)
⟹
a
x
2
+
b
x
+
c
=
a
x
2
−
a
(
α
+
β
)
x
+
a
α
β
where:
α
and
β
are the two roots of the equation.
Comparing the coefficients on both sides,
b
=
−
a
(
α
+
β
)
⟹
α
+
β
=
−
b
a
also
c
=
a
α
β
⟹
α
β
=
c
a
So from here,
The sum of the roots is equal to
=
α
+
β
=
−
b
a
Product of the roots is equal to
=
α
β
=
c
a