Tiêu đề Maths XII - Quadratic equations - Solving quadratic inequations .ppt.ppt ✅

SOLVING QUADRATIC INEQUATIONS
QUADRATIC INEQUATIONS If ax2+bx+c is a quadratic expression, then ax2+bx+c>0, ax2+bx+c ≥0, ax2+bx+c<0, ax2+bx+c≤0 are called quadratic inequations or quadratic inequalities. Example: 4x2+5x-1≥0, x2-2x-3<0 are quadratic inequations NOTE If α < β, then 1) (x-α)(x-β)≤0 ⇒ x∈[α,β] 2) (x-α)(x-β)≥0 ⇒x∈(-∞,α]∪[β, ∞) 3) (x-α)(x-β)<0 ⇒ x∈(α,β) 4) (x-α)(x-β)>0 ⇒x∈(-∞,α)∪(β, ∞)
METHODS OF SOLVING INEQUATIONS There are two methods for solving inequations. 1) Algebraic method : In this method we find the solutions by observing the changes in sign of the quadratic expression.