Theory of Intelligence
A-LEVEL•Mathematics•Quadratics•Question 3

Solution

🟢 Foundation · [3 marks] Solve the inequality $3x^2 - 5x - 2 > 0$.

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Solution

Factorise to find the critical values:

3x2−5x−2=(3x+1)(x−2)3x^2 - 5x - 2 = (3x + 1)(x - 2)

The critical values are x=−13x = -\tfrac13 and x=2x = 2. The curve is "U"-shaped, so it is above the axis outside the roots:

x<−13orx>2x < -\tfrac13 \quad\text{or}\quad x > 2

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