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Quadratic equation formulas class 11

Answer»

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, if

(a) D < => COMPLEX roots

(b) D > 0 => Real and distinct roots

(c) D = 0 => Real and equal roots as α = β = – b/2a

(ii) If a, b, C ∈ Q, a ≠ 0, then

(a) If D > 0 and D is a PERFECT square => Roots are unequal and rational.

(b) If D > 0, a = 1; b, c ∈ I and D is a perfect square. => Roots are integral. .

(c) If D > and D is not a perfect square. => Roots are irrational and unequal.


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