Edexcel IGCSE Math A 2.8.HA Quadratic Inequalities

Practise solving one-variable quadratic inequalities by finding boundary roots and selecting the intervals with the required sign.

Exam points

factorise or solve the boundary quadratic to identify its critical values
test the sign between and outside the roots before selecting solution intervals
include a root only when the original inequality contains equality

[Maximum number: 3]

Solve the inequality $2 y^{2}-7 y-30 \leqslant 0$

Show your working clearly.

Solve the associated quadratic:
$2y^2-7y-30=0$ (2y+5)(y-6)=0

Critical values:
$y=-2.5,\quad y=6$

Since the quadratic is less than or equal to zero between the roots,
$-2.5\leq y\leq6$

Final answer:
$-2.5\leq y\leq6$

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2.8.HA Solving quadratic inequalities question 1