A-LEVEL•Mathematics•Quadratics•Question 8

Solution

🟡 Exam-style · [5 marks] The line $y = x + 1$ meets the curve $y = 2x^2 - 3x - 5$ at the points $A$ and $B$. Find the coordinates of $A$ and $B$, and find the exact length of $AB$.

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Solution

\begin{aligned} 2x^2 - 3x - 5 &= x + 1 \\ 2x^2 - 4x - 6 &= 0 \\ x^2 - 2x - 3 &= 0 \\ (x - 3)(x + 1) &= 0 \end{aligned}

So $x = -1$ or $x = 3$ . Using the line, $A(-1,\ 0)$ and $B(3,\ 4)$ .

AB = \sqrt{(3 - (-1))^2 + (4 - 0)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}

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