Solve this quadratic equation by factorisation method
1)3x2-2√6+2=0
2) 7m2=21m
3) m2-11=0
Answers
Step-by-step explanation:
(1) x2 + 5x – 2 = 0
Only one variable x.
Maximum index = 2
So, it is a quadratic equation.
(2) y2 = 5y – 10
Only one variable y.
Maximum index = 2
So, it is a quadratic equation.
(3) y2+
1
y
=2
⇒y3+1=2y
Only one variable y.
Maximum index = 3
So, it is not a quadratic equation.
(4) x+
1
x
=-2
⇒x2+1=-2x
Only one variable x.
Maximum index = 2
So, it is a quadratic equation.
(5) (m + 2) (m – 5) = 0
⇒m2-3m-10=0
Only one variable m.
Maximum index = 2
So, it is a quadratic equation.
(6) m3 + 3m2 – 2 = 3m3
Only one variable m.
Maximum index = 3
So, it is not a quadratic equation.
Answer:
1) Given: 3x
2
−2
6
x+2=0
3x
2
−
6
x−
6
x+2=0,
3
x(
3
x−
2
)−
2
(
3
x−
2
)=0
(
3
x−
2
)(
3
x−
2
)=0∴
3
x−
2
=0 or
3
x−
2
=0
∴
3
x=
2
or
3
x=
2
,x=
3
2
or x=
3
2
So, the root is repeated twice, one for each repeated factor (
3
x−
2
)l.
∴ The two equal roots of 3x
2
−2
6
x+2=0 are
3
2
,
3
2
2) 7
2
=
2
1
7
2
−
(
2
1
)
=
0
3) M
2
−11M+10
⇒M
2
−10M−M+10
⇒M(M−10)−1(M−10)
⇒(M−10)(M−1)
∴M
2
−11M+10=(M−1)(M−10).
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