mat 1997 Q2

mat · Uk 15 marks Inequalities Simultaneous/Compound Quadratic Inequalities
(a) Show that $x ^ { 2 } + 4 x + 4 \geq 0$ for all values of $x$.\ (b) For which values of the constant $a$ is there at least one solution, $x$, of the inequality
$$a x ^ { 2 } + 4 x + 3 \leq x ^ { 2 } - 1 ?$$
(c) Suppose that $1 < a \leq 2$. Find all values of $x$ for which the inequality in (b) holds. 
(a) Show that $x ^ { 2 } + 4 x + 4 \geq 0$ for all values of $x$.\
(b) For which values of the constant $a$ is there at least one solution, $x$, of the inequality

$$a x ^ { 2 } + 4 x + 3 \leq x ^ { 2 } - 1 ?$$

(c) Suppose that $1 < a \leq 2$. Find all values of $x$ for which the inequality in (b) holds.
Paper Questions
Q1 Q2 Q3 Q4 Q5