Quadratic Equations — Question Ex 4.1 Q2
Back to all questionsRepresent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
CBSE Class 10 Quadratic Equations — Complete Guide
Quadratic Equations is one of the highest-weightage chapters (5-7 marks). The quadratic formula and nature of roots are tested every year without exception.
Quick Revision: Key Concepts
- Standard form: ax² + bx + c = 0, a ≠ 0
- Factorisation: Split middle term (product = ac, sum = b)
- Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
- Discriminant D = b² − 4ac: D > 0 (two roots), D = 0 (equal roots), D < 0 (no real roots)
- Word problems: Always check validity of both roots
Most Important Questions
- Solve by factorisation and quadratic formula
- Find k for which equation has equal/real/no real roots
- Word problems: consecutive numbers, area, speed-distance-time
- Nature of roots determination
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