- A40
- B36
- C44
- D80
Step-by-Step Solution
= (−5 ± 85)/2 → or −45. Speed must be positive, so 40 km/h.
Answer: A) 40
Solve the train equation . The valid speed (in km/h) is ____.
Class 10Quadratic EquationsAlgebra — Quadratics
Key idea: Word problems with quadratics
Many real-world problems lead to quadratics:
**Number problems**: 'Find two consecutive integers whose product is 132.' Let ; → → or −12. Both valid (or pick positive).
**Area problems**: 'A garden's length is 5 m more than its width. Area is . Find dimensions.'
Let width = . Length = → → (rejecting negative).
**Speed/time/distance**: 'A train takes 1 hour less if its speed is increased by 10 km/h. Original speed?' → typical setup: time1 − time2 = 1 → distance/speed equations → quadratic in speed.
**Always**: reject negative or extraneous roots if context demands positive (lengths, ages, speeds).
**Number problems**: 'Find two consecutive integers whose product is 132.' Let ; → → or −12. Both valid (or pick positive).
**Area problems**: 'A garden's length is 5 m more than its width. Area is . Find dimensions.'
Let width = . Length = → → (rejecting negative).
**Speed/time/distance**: 'A train takes 1 hour less if its speed is increased by 10 km/h. Original speed?' → typical setup: time1 − time2 = 1 → distance/speed equations → quadratic in speed.
**Always**: reject negative or extraneous roots if context demands positive (lengths, ages, speeds).
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