QUADRATIC EQUATIONS
Sol:
iii)
(k –12)x2
+
2 (k – 12) x
+
=
0
2
The given quadratic equation is
(k –12)x2
+
2 (k – 12) x
+
=
0
2
Comparing with
ax2
+
bx
+
c
=
0
We have
a
=
k –12,
b
=
2 (k –12),
c
=
2
Q
The roots of given equation are real
and equal.
∴
b2
–
4ac
=
0
∴
4(k – 12)2
–
8(k – 12)
=
0
∴
Dividing throughout by 4,
(k – 12)2
–
2 (k – 12)
=
0
∴
(k – 12)
k – 12
=
0
∴
(k – 12)
(k – 14)
=
0
We know that in
ax2
+
bx
+
c
=
0
a ≠ 0
∴
a
=
k – 12
∴
k – 12
≠
0
∴
k – 14
=
0
∴
k
=
14
∴
The value of k is 14.
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
(
)
[ ]2
= 0
2(k – 12)
(k – 12)
(2)
∴
– 4