Example 1 · level 1
Solve x² + x − 20 = 0. Give the larger root.
Show solution
- x² + x − 20 = (x − 4)(x + 5)
- x − 4 = 0 → x = 4; x + 5 = 0 → x = −5.
- The larger root is 4.
Answer: 4
CLASS 10 MATHS · QUADRATIC EQUATIONS
Solve quadratic equations by factorisation
Split the middle term (find two numbers with product ac and sum b), factorise, then set each factor to zero.
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Worked examples
Example 2 · level 2
Solve 2x² + 16x − 18 = 0. Give the smaller root.
Show solution
- 2x² + 16x − 18 = 2(x − 1)(x + 9)
- x − 1 = 0 → x = 1; x + 9 = 0 → x = −9.
- The smaller root is −9.
Answer: -9
Example 3 · level 3
A rectangular plot in Nagpur has area 160 m². Its length is 6 m more than its breadth. Find the breadth (in m).
Show solution
- x² + 6x − 160 = 0
- (x + 16)(x − 10) = 0
- x = 10 m (a length cannot be negative). Length = 16 m.
Answer: 10 m