foctorise X^2-8x+20 . please tell me .is this question right. if yes please tell me the answer
Answers
Answer:
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
1
⋅
−
20
=
−
20
AND
N
1
+
N
2
=
b
=
−
8
After trying out a few numbers we get
N
1
=
2
and
N
2
=
−
10
2
⋅
(
−
10
)
=
−
20
, and
2
+
(
−
10
)
=
−
8
x
2
−
8
x
−
20
=
x
2
−
10
x
+
2
x
−
20
=
x
(
x
−
10
)
+
2
(
x
−
1
0
)
(
x
+
2
)
(
x
−
10
)
is the factorised form of the expression.
x²-8x+20=0.....(Given Quadratic equation)
Comparing the above equation with ax²+bx+c=0, we get...
a=1 ,b= -8 and c=20
b²-4ac=(-8)²-4×1×20
=64-80
= -20
x=-b±√b²-4ac/2a
x= 8±√-20/2
Therefore, x=8+√-20/2 or
x=8-√-20/2.....(As per your question)
Correct Question:
Factorise:x²-8x-20=0
Solution:
x²-8x-20=0
x²-10x+2x-20=0
x(x-10) +2(x-10) =0
(x+2) (x-10) =0
(x+2) =0 Or (x-10) =0
x=-2 Or x=10
Therefore,