Algebra
Complex numbers, quadratics, sequences and series, binomial theorem, and matrices
Key Concepts
- Complex numbers: modulus, argument and the Argand plane
- Quadratics: the discriminant decides the nature of the roots
- Sequences and series: arithmetic and geometric progressions
- Binomial theorem for any positive integral index
- Matrices and determinants for solving linear systems
Important Formulae
| Quadratic roots | x = (−b ± √(b²−4ac))/2a |
| Sum & product of roots | α+β = −b/a; αβ = c/a |
| AP sum | S_n = n/2 [2a + (n−1)d] |
| GP sum | S_n = a(rⁿ−1)/(r−1); S_∞ = a/(1−r), |r|<1 |
| Binomial term | T_{r+1} = ⁿC_r a^{n−r} b^r |
Quick Tips
- Discriminant: D>0 real & distinct, D=0 equal, D<0 complex conjugate roots.
- |z|² = z·z̄; multiplying complex numbers adds their arguments.
- The n nth-roots of unity sum to zero.
Sample Practice Questions
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The sum of the roots of x² − 7x + 12 = 0 is:
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Answer: 7
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The number of terms in the binomial expansion of (a + b)ⁿ is:
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Answer: n + 1
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The sum of the first 10 natural numbers is:
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Answer: 55
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The discriminant of x² − 5x + 6 is:
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Answer: 1
Practice Questions
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What are the key concepts in Algebra for JEE?
Complex numbers: modulus, argument and the Argand plane; Quadratics: the discriminant decides the nature of the roots; Sequences and series: arithmetic and geometric progressions; Binomial theorem for any positive integral index; Matrices and determinants for solving linear systems.
Which formulae are important for Algebra in JEE?
Quadratic roots: x = (−b ± √(b²−4ac))/2a; Sum & product of roots: α+β = −b/a; αβ = c/a; AP sum: S_n = n/2 [2a + (n−1)d]; GP sum: S_n = a(rⁿ−1)/(r−1); S_∞ = a/(1−r), |r|<1; Binomial term: T_{r+1} = ⁿC_r a^{n−r} b^r.
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