Math Pro
about
qns
questions
progress
Question 0101c
Equations and Inequalities
Inequalities III
Question
Generate new
What is the approach to solving exactly the inequality
x
2
+
5
x
+
25
x
−
9
>
0
?
\frac{x^2 + 5 x + 25}{x - 9} > 0?
x
−
9
x
2
+
5
x
+
25
>
0
?
Attempt
Select the correct option:
Use the quadratic formula
x
=
−
b
±
b
2
−
4
a
c
2
a
{x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}
x
=
2
a
−
b
±
b
2
−
4
a
c
for
x
2
+
5
x
+
25
=
0
{x^2 + 5 x + 25=0}
x
2
+
5
x
+
25
=
0
to find the critical points.
"Cross multiply" by multiplying
x
−
9
{x - 9}
x
−
9
to the RHS of the equation.
Factorize
x
2
+
5
x
+
25
{x^2 + 5 x + 25}
x
2
+
5
x
+
25
into the form
(
x
+
p
)
(
x
+
q
)
{(x+p)(x+q)}
(
x
+
p
)
(
x
+
q
)
to find the critical points.
Complete the square for
x
2
+
5
x
+
25
{x^2 + 5 x + 25}
x
2
+
5
x
+
25
into the form
(
x
+
p
)
2
+
q
{(x+p)^2 + q}
(
x
+
p
)
2
+
q
to show that it is always positive.
Answer
Back to top ▲
Question Progress
Start
Mastery
about
questions
progress