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Quadratic Equation
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Quadratic Equation
- Roots of a Quadratic Equation Quadratic Equation Polynomial Equation Degree of a Polynomial Complex Polynomial: Real Polynomial:
Solution of Quadratic Equation
- Factorization Method:
- Let ax2 + bx + c = α(x – α) (x – β) = O. Then, x = α and x = β will satisfy the given equation.
- Direct Formula
- Quadratic equation ax2 + bx + c = 0 (a ≠ 0) has two roots,
- Quadratic equation ax2 + bx + c = 0 (a ≠ 0) has two roots,
- Factorization Method:
Nature of Roots
- Let quadratic equation be ax2 + bx + c = 0, whose discriminant is D. (i) For ax2 + bx + c = 0; a, b , C ∈ R and a ≠ 0,
- (a) D < => Complex roots (b) D > 0 => Real and distinct roots (c) D = 0 => Real and equal roots as α = β = – b/2a
- Let quadratic equation be ax2 + bx + c = 0, whose discriminant is D. (i) For ax2 + bx + c = 0; a, b , C ∈ R and a ≠ 0,