# Inequality

```1. Find the set of values of π₯ or find the range of values of π₯ which satisfy the inequalities:
a) π₯(π₯ − 2) &lt; 3
e) (π₯ − 1)(5π₯ + 4) ≤ 2(π₯ − 1)
b) π₯ 2 + 5π₯ − 6 &lt; 0
c) π₯ 2 &gt; 4π₯ + 12
d) 4π₯(π₯ + 1) ≤ 3
g) (π₯ + 2)2 &lt; π₯(4 − π₯) + 40
2. The roots of the equation (π + 2)π₯ 2 − 2ππ₯ = 5 − π are not real; find the range of values of π.
3. Find the range of values of π for which the equation 2π₯ 2 + 5π₯ + 3 − π = 0 has two real distinct roots.
4. Find the set of values of the constant k for which the equation 2π₯ 2 − ππ₯ + 2π = 6 has real roots.
5. Given that the equation π₯ 2 − 12π₯ − 6 = 0 has roots πΌ and π½.
Find
a) πΌ + π½ and πΌπ½
b) (πΌ + π½)2
c) (πΌ − π½)2
6. Given that the roots of the equation 3π₯ 2 + ππ₯ + 4 = 0 are πΌ and 3πΌ. Find the two possible values of π.
7. Given that the equation π₯ 2 − 2π₯ − 3 = π, where π is a constant, has repeated roots. Find the value of π.
8. Given that the equation 4π₯ 2 + ππ₯ + 2π = 15, where π is a positive constant. Find the values of π for which
this equation has equal roots.
9. Complete the square of the following expressions:
a) π₯ 2 − 9π₯ − 72
b) 2π₯ 2 − 10π₯ − 19
```