=======================================================
Explanation:
I'm assuming you meant to type 8x^2 + bx + 2 = 0
Compare this to ax^2 + bx + c = 0
We have a = 8, b = unknown, c = 2.
We'll use the discriminant formula which is D = b^2 - 4ac to find that
D = b^2 - 4ac
D = b^2 - 4*8*2
D = b^2 - 64
Since we want one real solution, we set the discriminant equal to zero.
D = b^2 - 64
0 = b^2 - 64
64 = b^2
b^2 = 64
b = sqrt(64) or b = -sqrt(8)
b = 8 or b = -8
So the equation 8x^2 + 8x + 2 = 0 has one solution. So does the equation 8x^2-8x+2 = 0
Answer:
To find the value of
b
where there will be just ONE soluition, we set the discriminate equal to
0
, substitute for
a
and
c
and solve for
b
:
Substitute:
2
for
a
−
b
for
b
−
9
for
c
−
b
2
−
(
4
⋅
2
⋅
−
9
)
=
0
−
b
2
−
(
−
72
)
=
0
−
b
2
+
72
=
0
−
b
2
+
72
−
72
=
0
−
72
−
b
2
+
0
=
−
72
−
b
2
=
−
72
−
1
⋅
−
b
2
=
−
1
⋅
−
72
b
2
=
72
√
b
2
=
±
√
72
b
=
±
√
36
⋅
2
b
=
±
√
36
√
2
b
=
±
6
√
2To find the value of
b
where there will be just ONE soluition, we set the discriminate equal to
0
, substitute for
a
and
c
and solve for
b
:
Substitute:
2
for
a
−
b
for
b
−
9
for
c
−
b
2
−
(
4
⋅
2
⋅
−
9
)
=
0
−
b
2
−
(
−
72
)
=
0
−
b
2
+
72
=
0
−
b
2
+
72
−
72
=
0
−
72
−
b
2
+
0
=
−
72
−
b
2
=
−
72
−
1
⋅
−
b
2
=
−
1
⋅
−
72
b
2
=
72
√
b
2
=
±
√
72
b
=
±
√
36
⋅
2
b
=
±
√
36
√
2
b
=
±
6
√
2
Step-by-step explanation:
