Ch 4 covers solving quadratic equations by factorisation, completing the square, and the quadratic formula. Students learn to determine the nature of roots using the discriminant without actually solving.
Write ax² + bx + c = 0, split the middle term bx into two terms whose product equals ac × x². Factor by grouping. If (px + q)(rx + s) = 0, then x = −q/p or x = −s/r.
For ax² + bx + c = 0: x = (−b ± √(b²−4ac)) / 2a. This formula always works and is derived by completing the square. The discriminant D = b² − 4ac determines the nature of roots.
D > 0: two distinct real roots. D = 0: two equal (repeated) real roots. D < 0: no real roots (roots are complex). This allows us to determine root nature without solving.
Download: https://ncert.nic.in/textbook/pdf/jemh104.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
The discriminant D = b² − 4ac reveals the nature of roots without solving: D > 0 means 2 distinct real roots, D = 0 means 2 equal real roots, and D < 0 means no real roots exist.
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