Master Unit 2 Quadratic Equations (NBF/FBISE new book 2025-2026) with concise solutions. Aim 90+ marks.
hsanotes.com Features:
- Updated for new book session 2025-2026
- Solved Ex 2.1–2.4 + Miscellaneous
- Standard form conversions
- Factoring, completing square methods
- Quadratic formula applications
- Discriminant analysis, nature of roots
- Graphs of quadratics
- Word problems solutions
Target: FBISE students & affiliated schools – Army Public School, Fazaia Inter College, Beaconhouse, Roots Millennium, The City School, Lahore Grammar School, Karachi Grammar School, OPF Boys/Girls College, Bahria College, PAF College.
Key Solved Examples (short form):
- Ex 2.1 Q1(i) (x+2)(x-3)=5 → x² – x – 11=0
- Q1(ii) (x-5)² – (2x+4)²=7 → 3x² + 26x – 2=0
- Q1(iii) x = x(x-1) → x² – 2x=0
- Q2(i) (x-1)(x-4)=0 → x=1,4
- Q2(ii) x² – 2x +1=0 → x=1 (repeated)
- Q2(iii) x² -7x -8=0 → x=8,-1
- Q2(iv) x² -4x +4=(2x-7)² → x=5,3
- Q2(v) [(2x+7)/4]² = (48x²+529)/16 → x=-10,3
- Q3(i) x² +4x -32=0 → x=4,-8
- Q3(ii) x² +8x=0 → x=0,-8
- Q3(iii) x² +6x -9=0 → x=-3±3√2
- Q3(iv) 3x² +12x +8=0 → x=(-6±2√3)/3
- Q3(v) x² +x +1=0 → x=(-1±i√3)/2
- Q3(vi) 4x² -8x -5=0 → x=5/2,-1/2
- Q4(i) x² -9=0 → x=3,-3
- Q4(ii) 2x² +5x +1=0 → x=(-5±√17)/4
- Q4(iii) x² -23x -24=0 → x=24,-1
- Q4(iv) (x+1)²=(2x-1)² → x=2,0
- Q4(v) (x+1)/2 – x(x+2)/2=0 → x=(-1±√5)/2
- Q4(vi) (x-2)(x-6)=(2x+1)(x+1) → x=(-11±√165)/2
Useful Links:
- FBISE official: https://www.fbise.edu.pk
- National Book Foundation (NBF): https://www.nbf.org.pk
- Army Public Schools: https://apsacssectt.edu.pk
- Beaconhouse: https://www.beaconhouse.net
View PDF for full solutions, graphs & tables.
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