Maths · Algebra · chapter 4 of 14
Class 10 Maths Chapter 4: Quadratic Equations case study question with answers
One case-based question of the kind the board asks in Section E: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A gram panchayat near Hassan is fencing a rectangular plot for a community vegetable garden. The surveyor notes that the length of the plot is 6 m more than its breadth and that its area is 160 m². The panchayat needs the dimensions to order the fencing wire and to plan the beds. Let the breadth of the plot be x metres.
Part 1 · 1 mark
The quadratic equation satisfied by x is
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Answer: (a) x2 + 6x − 160 = 0
Length x + 6, area x(x + 6) = 160, so x2 + 6x − 160 = 0.
Part 2 · 1 mark
The discriminant of this equation is
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Answer: (a) 676
D = 62 − 4 × 1 × (−160) = 36 + 640 = 676.
Part 3 · 2 marks
Find the length and breadth of the plot.
Answer and marking scheme
x = (−6 ± √676)/2 = (−6 ± 26)/2, so x = 10 or x = −16. A breadth cannot be negative, so the breadth is 10 m and the length is 16 m.
- solves to x = 10 or −16 (1)
- rejects −16; breadth 10 m, length 16 m (1)
Or
Find the length of wire needed to fence the plot once around.
Answer and marking scheme
x2 + 6x − 160 = 0 gives (x + 16)(x − 10) = 0; breadth 10 m (−16 rejected), length 16 m. Perimeter = 2(16 + 10) = 52 m.
- finds breadth 10 m, length 16 m, rejecting −16 (1)
- perimeter 52 m (1)
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