QUADRATIC EQUATIONS
Sol:
iv)
k2x2
–
2 (k – 1) x
+
=
0
4
The given quadratic equation is
k2x2
–
2 (k – 1) x
+
=
0
4
Comparing with
ax2
+
bx
+
c
=
0
We have
a
=
k2,
b
=
–2 (k –1),
c
=
4
Q
The roots of given equation are real
and equal.
∴
b2
–
4ac
=
0
∴
–2(k – 1)
–
(k2)
(4)
=
0
∴
4(k – 1)2
–
16k2
=
0
∴
Dividing throughout by 4, we get
(k – 1)2
–
4 k2
=
0
∴
(k – 1)2
–
(2k)2
=
0
∴
(k – 1 + 2k)
(k – 1 – 2k)
=
0
∴
(3k – 1 )
(– k – 1)
=
0
∴
3k – 1
=
0
or
– k – 1
=
0
∴
3k
=
1
or
– k
=
1
∴
k
=
or
k
=
–1
The given information is b2-4ac = 0
So we need to find the values of a, b & c
For that the equation should be in a standard form
Is it in a standard form ?
Yes
Find the value of k for which given equation has real and equal roots.
[ ]2
4
homework