2x^2-√3x+9 factorise it
Answers
Step-by-step explanation:
The rule to factorise any quadratic is to find two numbers such that
product
=
x
2
coefficient
×
constant coefficient
sum
=
x
coefficient
So for
2
x
2
−
3
x
−
9
we seek two numbers such that
product
=
(
2
)
⋅
(
−
9
)
=
−
18
sum
=
−
3
So we look at the factors of
−
18
. As the product is negative one of the factors must also be negative and the other positive, We compute their sum we get
factor1
factor2
sum
18
−
1
17
9
−
2
7
6
−
3
3
−
18
1
−
17
−
9
2
−
7
−
6
3
−
3
So the factors we seek are
−
6
and
3
Therefore we can factorise the quadratic as follows:
2
x
2
−
3
x
−
9
=
2
x
2
−
6
x
+
3
x
−
9
∴
2
x
2
−
3
x
−
9
=
2
x
(
x
−
3
)
+
3
(
x
−
3
)
∴
2
x
2
−
3
x
−
9
=
(
2
x
+
3
)
(
x
−
3
)
This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.
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Answer:
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