Question 1: Solve the following quadratic equations by factorization method:
i) ii)
iii) iv)
Answer:
i)
So the roots of given quadratic equation are and
ii)
So the roots of given quadratic equation are and
iii)
or
So the roots of given quadratic equation are and
iv)
or
So the roots of given quadratic equation are
and
Question 2: Solve the following quadratic equations:
i) ii)
iii) iv)
v) vi)
vii)
viii) ix)
x) xi)
xii)
Answer:
i)
So the roots of given quadratic equation are and
ii)
So the roots of given quadratic equation are and
iii)
or
iv)
or
v)
vi)
vii)
Comparing the given equation with general form of quadratic equation we get,
Substituting these values in
Therefore
Now lets calculate the roots of
Let
Squaring both sides
… … … … … i)
and … … … … … ii)
We know
… … … … … iii)
Adding i) and iii) we get
Substituting in i) we get
Since is positive,
and
will have the same sign.
if
and if
and
viii)
Comparing the given equation with general form of quadratic equation we get,
Substituting these values in
Therefore
Now lets calculate the roots of
Let
Squaring both sides
… … … … … i)
and … … … … … ii)
We know
… … … … … iii)
Adding i) and iii) we get
Substituting in i) we get
Since is negative,
and
will have opposite sign.
if
and if
and
ix)
x)
Comparing the given equation with general form of quadratic equation we get,
Substituting these values in
Therefore
Now lets calculate the roots of
Let
Squaring both sides
… … … … … i)
and … … … … … ii)
We know
… … … … … iii)
Adding i) and iii) we get
Substituting in i) we get
Since is negative,
and
will have opposite sign.
if
and if
Hence the roots of the equation are
xi)
Comparing the given equation with general form of quadratic equation we get,
Substituting these values in
Therefore
xii)